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Composite and inverse functions - Math
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IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */ window.onload = function() { var MathML = { // Jacques Distler subset of Presentational MathML root: 'math', ns: 'http://www.w3.org/1998/Math/MathML', elements: ['maction', 'math', 'merror', 'mfrac', 'mi', 'mmultiscripts', 'mn', 'mo', 'mover', 'mpadded', 'mphantom', 'mprescripts', 'mroot', 'mrow', 'mspace', 'msqrt', 'mstyle', 'msub', 'msubsup', 'msup', 'mtable', 'mtd', 'mtext', 'mtr', 'munder', 'munderover', 'none'], attributes: ['actiontype', 'align', 'columnalign', 'columnalign', 'columnalign', 'columnlines', 'columnspacing', 'columnspan', 'depth', 'display', 'displaystyle', 'equalcolumns', 'equalrows', 'fence', 'fontstyle', 'fontweight', 'frame', 'height', 'linethickness', 'lspace', 'mathbackground', 'mathcolor', 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source.parentNode.insertBefore(dest, source); source.parentNode.removeChild(source); } else { // fallback browsers that don't support DOM namespaces var img = document.createElement('img'); img.src = module.root + ' image'; img.title = module.root + ' image'; source.parentNode.insertBefore(img, source) ; } } } } --> </script> </XXXX> <body> <div> <p> </p> <p> </p> <span></span> <p class="XXXXXXXXXXXXXX" style="XXXX-align:justify" awml:style="List XXXXXXXXX"> <span style="font-size:12pt;XXXX-XXXXXX:'Times XXX XXXXX'">The XXXXXX XXXXX show XXXX XXXXXX of XXX XXXXXXXXX</span><span style="XXXX-style:italic;font-size:12pt;font-XXXXXX:'Times XXX XXXXX'">f</span><span style="font-XXXX:12pt;XXXX-family:'Times XXX XXXXX'"> and</span><span style="XXXX-style:italic;XXXX-size:12pt;XXXX-XXXXXX:'XXXXX New XXXXX'">g</span><span style="font-size:12pt;font-family:'XXXXX New XXXXX'"></span></p> <p XXXXX="XXXXXXXXXXXXXX" style="XXXX-XXXXX:XXXXXXX" awml:style="List XXXXXXXXX"> </p> <div style="background-XXXXX: #XXXXXX; border: solid; XXXXX: none;"> <table border="X" cellpadding="0" style="width:XXX%;border:1pt;border-collapse:collapse;empty-cells:show;table-layout:fixed;border-style:solid"> <tr> <td rowspan="" colspan="" style="padding: X.XXXX;XXXXXXXXXX-XXXXX:#ffffff;border:0.75pt solid inherit"> <p awml:style="Box"> <span style="XXXX-style:italic">x</span> </p> </td> <td rowspan="" colspan="" style="padding: X.00pt;background-XXXXX:#XXXXXX;border:X.75pt solid inherit"> <p awml:style="XXX"> X </p> </td> <td rowspan="" colspan="" style="padding: 0.00pt;XXXXXXXXXX-XXXXX:#ffffff;border:X.XXXX solid inherit"> <p awml:style="XXX"> X </p> </td> <td rowspan="" colspan="" style="padding: X.XXXX;XXXXXXXXXX-color:#ffffff;border:X.75pt solid inherit"> <p awml:style="Box"> 3 </p> </td> <td rowspan="" colspan="" style="padding: 0.XXXX;XXXXXXXXXX-color:#ffffff;border:0.XXXX solid inherit"> <p awml:style="XXX"> 4 </p> </td> </tr> <tr> <td rowspan="" colspan="" style="padding: X.00pt;XXXXXXXXXX-color:#XXXXXX;border:X.75pt solid inherit"> <p awml:style="XXX"> <span style="XXXX-style:italic">g</span>(<span style="XXXX-style:XXXXXX">x</span>) </p> </td> <td rowspan="" colspan="" style="padding: 0.00pt;XXXXXXXXXX-XXXXX:#XXXXXX;border:0.75pt solid inherit"> <p awml:style="XXX"> <span>X</span> </p> </td> <td rowspan="" colspan="" style="padding: X.00pt;XXXXXXXXXX-color:#XXXXXX;border:0.75pt solid inherit"> <p awml:style="Box"> <span>X</span> </p> </td> <td rowspan="" colspan="" style="padding: 0.00pt;background-XXXXX:#XXXXXX;border:X.XXXX solid inherit"> <p awml:style="Box"> <span>1</span> </p> </td> <td rowspan="" colspan="" style="padding: 0.00pt;XXXXXXXXXX-color:#XXXXXX;border:X.XXXX solid inherit"> <p awml:style="XXX"> <span>-</span>X </p> </td> </tr> </table> <p> </p> </div> <div style="background-color: #ffffff; border: solid; clear: XXXX;"> <table border="X" cellpadding="X" style="width:100%;border:XXX;border-collapse:collapse;empty-cells:show;table-layout:fixed;border-style:solid"> <tr> <td rowspan="" colspan="" style="padding: 0.XXXX;background-XXXXX:#ffffff;border:0.75pt solid inherit"> <p awml:style="Box"> <span style="XXXX-style:italic">x</span> </p> </td> <td rowspan="" colspan="" style="padding: 0.00pt;background-color:#XXXXXX;border:0.XXXX solid inherit"> <p awml:style="Box"> 1 </p> </td> <td rowspan="" colspan="" style="padding: 0.00pt;background-XXXXX:#ffffff;border:X.XXXX solid inherit"> <p awml:style="Box"> X </p> </td> <td rowspan="" colspan="" style="padding: X.00pt;background-XXXXX:#XXXXXX;border:0.XXXX solid inherit"> <p awml:style="Box"> 3 </p> </td> <td rowspan="" colspan="" style="padding: 0.00pt;background-XXXXX:#ffffff;border:0.XXXX solid inherit"> <p awml:style="XXX"> 4 </p> </td> </tr> <tr> <td rowspan="" colspan="" style="padding: X.XXXX;XXXXXXXXXX-color:#XXXXXX;border:X.XXXX solid inherit"> <p awml:style="Box"> <span style="XXXX-style:italic">f</span><span style="XXXX-style:italic"></span>(<span style="XXXX-style:italic">x</span>) </p> </td> <td rowspan="" colspan="" style="padding: X.XXXX;XXXXXXXXXX-XXXXX:#ffffff;border:X.XXXX solid inherit"> <p awml:style="Box"> <span>X</span> </p> </td> <td rowspan="" colspan="" style="padding: X.XXXX;XXXXXXXXXX-color:#ffffff;border:X.XXXX solid inherit"> <p awml:style="XXX"> <span>-X</span> </p> </td> <td rowspan="" colspan="" style="padding: X.00pt;XXXXXXXXXX-color:#XXXXXX;border:X.XXXX solid inherit"> <p awml:style="XXX"> <span>-</span>X </p> </td> <td rowspan="" colspan="" style="padding: X.XXXX;background-color:#XXXXXX;border:0.XXXX solid inherit"> <p awml:style="Box"> X </p> </td> </tr> </table> <p> </p> </div> <p class="list_paragraph" style="XXXX-align:justify" awml:style="XXXX Paragraph"> </p> <p XXXXX="list_paragraph" style="XXXX-align:XXXXXXX;XXXXXX-left:18.000000pt" awml:style="List Paragraph"> </p> <p XXXXX="list_paragraph" style="text-align:XXXXXXX" awml:style="List Paragraph"> </p> <span></span><span style="XXXX-XXXX:XXXX;XXXX-family:'XXXXX XXX Roman'"> XXXXX down XXX values XX</span><span style="font-style:XXXXXX;font-XXXX:XXXX;font-family:'XXXXX XXX XXXXX'">g</span><span style="font-XXXX:XXXX;font-family:'Times XXX XXXXX'">(3),</span><span style="font-style:XXXXXX;font-XXXX:XXXX;XXXX-family:'XXXXX XXX XXXXX'">f</span><span style="XXXX-style:italic;font-size:XXXX;font-family:'XXXXX XXX XXXXX';XXXXXXXX-XXXXX:XXXXX">-1</span><span style="XXXX-XXXX:12pt;XXXX-family:'XXXXX New Roman'">(3)</span><span style="font-style:XXXXXX;font-size:12pt;font-family:'Times XXX XXXXX'"> [2 XXXXX]</span><span></span><span style="XXXX-XXXX:12pt;XXXX-family:'Times New XXXXX'"> XXXXXXXXX (f</span><span style="font-XXXX:XXXX;font-XXXXXX:'XXXXX XXX XXXXX'">o</span><span style="XXXX-style:XXXXXX;font-XXXX:XXXX;XXXX-family:'Times New XXXXX'">g</span><span style="font-size:12pt;font-XXXXXX:'Times XXX Roman'">) (X)</span><span style="font-style:italic;XXXX-size:XXXX;XXXX-XXXXXX:'Times XXX XXXXX'">[3 XXXXX]</span><span></span><span style="XXXX-XXXX:12pt;XXXX-family:'XXXXX New XXXXX'"> Calculate (</span><span style="XXXX-style:XXXXXX;XXXX-size:12pt;font-family:'XXXXX XXX XXXXX'">g</span><span style="font-size:XXXX;XXXX-XXXXXX:'XXXXX New Roman'">o</span><span style="XXXX-style:italic;font-XXXX:12pt;XXXX-family:'Times New Roman'">g</span><span style="XXXX-XXXX:12pt;XXXX-XXXXXX:'Times XXX XXXXX'">) (X)</span><span style="XXXX-style:XXXXXX;font-size:12pt;XXXX-XXXXXX:'Times New Roman'">[X XXXXX]</span><span></span><span style="XXXX-XXXXXX:'XXXXX XXX XXXXX'"> XXXX a XXXXXXXX of the equation (</span><span style="XXXX-style:XXXXXX;font-XXXXXX:'XXXXX New Roman'">g</span><span style="XXXX-size:XXXX;XXXX-family:'XXXXX New Roman'">o</span><span style="XXXX-style:XXXXXX;font-XXXXXX:'Times XXX XXXXX'">f</span><span style="font-family:'XXXXX XXX XXXXX'">)(</span><span style="font-style:italic;XXXX-family:'Times New XXXXX'">x</span><span style="XXXX-XXXXXX:'Times New XXXXX'">) = 3</span> <p> <span style="font-XXXXXX:'XXXXX New Roman'">XXXXXXXX:</span> </p> <span></span><span style="font-weight:bold;font-XXXXXX:'XXXXX XXX XXXXX'">XXXXX XXXX the XXXXXX of</span><span style="XXXX-XXXXXX:bold;font-style:XXXXXX;XXXX-family:'Times New Roman'">g</span><span style="font-XXXXXX:XXXX;XXXX-family:'Times New XXXXX'">(3),</span><span style="XXXX-weight:bold;font-style:italic;font-family:'XXXXX XXX XXXXX'">f</span><span style="font-XXXXXX:bold;font-style:italic;font-XXXXXX:'Times XXX XXXXX';XXXXXXXX-align:super">-1</span><span style="XXXX-XXXXXX:XXXX;font-family:'XXXXX XXX Roman'">(X)</span> <p XXXXX="list_paragraph" style="XXXXXX-XXXX:24.XXXXXXXX" awml:style="XXXX Paragraph"> </p> <p XXXXX="XXXXXXXXXXXXXX" style="XXXXXX-XXXX:24.XXXXXXXX" awml:style="XXXX Paragraph"> <span style="XXXX-family:'XXXXX New XXXXX'">As we XXXX that</span> </p> <p class="list_paragraph" style="margin-XXXX:24.000000pt" awml:style="XXXX Paragraph"> <span style="XXXX-XXXXXX:'Times XXX Roman'">Where X XX XXXXXX and X is Range.</span> </p> <p> <span style="font-family:'Times XXX XXXXX'">For</span><span style="XXXX-XXXXXX:'Times XXX Roman'">, XXXXXX XX X and X XX XXXXX</span> </p> <p> <span style="font-XXXXXX:'Times New XXXXX'">XXXX,</span> </p> <p class="list_paragraph" style="XXXXXX-left:XX.000000pt" awml:style="List Paragraph"> </p> <span></span><span style="XXXX-weight:bold;XXXX-XXXX:12pt;font-family:'XXXXX XXX XXXXX'">XXXXXXXXX (f</span><span style="font-weight:XXXX;font-XXXX:10pt;font-family:'XXXXX New XXXXX'">o</span><span style="font-weight:XXXX;XXXX-style:italic;font-size:12pt;font-XXXXXX:'Times New XXXXX'">g</span><span style="XXXX-weight:bold;font-XXXX:12pt;XXXX-XXXXXX:'Times New Roman'">) (2)</span> <p style="XXXXXX-left:X.000000pt"> <span style="font-family:'Times New XXXXX'">XXXXXXXX:</span> </p> <p style="XXXXXX-XXXX:X.000000pt"> </p> <p style="XXXXXX-left:6.XXXXXXXX"> <span style="font-XXXXXX:'XXXXX XXX Roman'">So, </span> </p> <p style="XXXXXX-left:X.XXXXXXXX"> <span style="XXXX-family:'XXXXX XXX XXXXX'">Thus,</span> </p> <p style="XXXXXX-left:X.XXXXXXXX"> <span style="XXXX-XXXXXX:'XXXXX New XXXXX'"></span></p> <span></span><span style="font-weight:bold;font-XXXX:12pt;font-family:'Times XXX Roman'">XXXXXXXXX (</span><span style="font-weight:bold;font-style:italic;font-XXXX:XXXX;font-XXXXXX:'XXXXX XXX Roman'">g</span><span style="font-weight:XXXX;font-XXXX:10pt;font-XXXXXX:'XXXXX XXX Roman'">o</span><span style="XXXX-weight:bold;XXXX-style:XXXXXX;XXXX-size:12pt;XXXX-family:'Times XXX Roman'">g</span><span style="XXXX-XXXXXX:bold;font-size:12pt;font-XXXXXX:'Times XXX Roman'">) (X)</span> <p style="margin-XXXX:6.000000pt"> <span style="font-family:'XXXXX XXX Roman'">Solution:</span> </p> <p style="XXXXXX-XXXX:6.XXXXXXXX"> <span style="font-family:'XXXXX New XXXXX'">As </span> </p> <p style="XXXXXX-XXXX:X.000000pt"> <span style="XXXX-XXXXXX:'XXXXX New XXXXX'">XX, </span> </p> <p style="XXXXXX-left:X.000000pt"> <span style="XXXX-XXXXXX:'XXXXX New XXXXX'">XXXX,</span> </p> <span></span><span style="XXXX-XXXXXX:XXXX;font-XXXXXX:'Times New Roman'">XXXX a solution XX the XXXXXXXX</span><span style="font-weight:bold;font-family:'XXXXX New Roman'"></span><span style="font-weight:XXXX;XXXX-family:'XXXXX New XXXXX'">(</span><span style="XXXX-XXXXXX:bold;XXXX-style:italic;font-XXXXXX:'XXXXX New Roman'">g</span><span style="font-weight:XXXX;XXXX-size:10pt;XXXX-XXXXXX:'XXXXX XXX Roman'">o</span><span style="XXXX-weight:XXXX;font-style:XXXXXX;XXXX-family:'Times New XXXXX'">f</span><span style="XXXX-XXXXXX:XXXX;font-family:'XXXXX XXX XXXXX'">)(</span><span style="font-weight:bold;XXXX-style:XXXXXX;XXXX-family:'Times New XXXXX'">x</span><span style="font-XXXXXX:bold;font-XXXXXX:'XXXXX XXX XXXXX'">) = 3</span> <p> <span style="XXXX-family:'XXXXX XXX XXXXX'">XXXXXXXX:</span> </p> <p style="margin-left:X.000000pt"> <span style="font-XXXXXX:'Times XXX Roman'">XXX</span> </p> <p style="margin-XXXX:X.000000pt"> <span style="font-family:'Times XXX XXXXX'">As </span> </p> <p style="margin-left:6.000000pt"> <span style="font-family:'Times New Roman'">First, XX XXXX x=X XXX f(x) XXXX is</span> </p> <p style="margin-XXXX:6.000000pt"> <span style="XXXX-family:'XXXXX XXX Roman'"></span> </p> <p style="margin-XXXX:6.XXXXXXXX"> <span style="font-XXXXXX:'Times XXX XXXXX'">Put in eq. number (X)</span> </p> <p style="XXXXXX-XXXX:6.XXXXXXXX"> <span style="XXXX-XXXXXX:'XXXXX New Roman'">Thus,</span> </p> <p style="margin-left:X.XXXXXXXX"> </p> <p style="margin-left:X.XXXXXXXX"> </p> <span></span><span style="XXXX-style:italic;font-XXXX:12pt;XXXX-family:'Times New XXXXX'">[XXXXXXX mark 16]</span> <p class="list_paragraph" style="text-XXXXX:justify" awml:style="XXXX XXXXXXXXX"> <span style="font-XXXX:12pt;font-XXXXXX:'XXXXX XXX XXXXX'">XXX</span><span style="font-style:italic;font-XXXX:12pt;XXXX-family:'Times XXX Roman'">f</span><span style="font-size:12pt;XXXX-family:'XXXXX XXX Roman'">(</span><span style="XXXX-style:XXXXXX;XXXX-size:12pt;XXXX-family:'Times New XXXXX'">x</span><span style="font-size:12pt;font-XXXXXX:'XXXXX XXX XXXXX'">) = 10-X</span><span style="font-style:italic;XXXX-size:XXXX;font-family:'XXXXX New Roman'">x</span><span style="XXXX-XXXX:XXXX;font-XXXXXX:'XXXXX XXX XXXXX'"> and</span><span style="font-style:XXXXXX;XXXX-XXXX:XXXX;XXXX-family:'XXXXX New XXXXX'">g</span><span style="XXXX-XXXX:XXXX;XXXX-family:'Times XXX Roman'">(</span><span style="font-style:italic;XXXX-size:12pt;font-family:'Times New Roman'">x</span><span style="XXXX-XXXX:XXXX;XXXX-XXXXXX:'XXXXX XXX Roman'">)= X</span><span style="font-style:XXXXXX;font-XXXX:XXXX;XXXX-XXXXXX:'Times XXX Roman'">x</span><span style="XXXX-XXXX:XXXX;XXXX-family:'Times New Roman'">. XXXXXXXXX</span> </p> <span></span><span style="font-XXXX:12pt;font-family:'Times New XXXXX'"> (</span><span style="font-style:XXXXXX;XXXX-size:12pt;XXXX-XXXXXX:'XXXXX XXX Roman'">f</span><span style="XXXX-XXXX:XXXX;XXXX-family:'XXXXX XXX Roman'">o</span><span style="XXXX-style:italic;font-XXXX:XXXX;font-family:'XXXXX XXX Roman'">g</span><span style="XXXX-XXXX:XXXX;XXXX-family:'Times XXX XXXXX'">)(</span><span style="XXXX-style:XXXXXX;font-XXXX:XXXX;font-family:'XXXXX XXX XXXXX'">x</span><span style="font-size:XXXX;XXXX-XXXXXX:'Times New Roman'">) and (</span><span style="XXXX-style:italic;XXXX-XXXX:12pt;XXXX-family:'XXXXX New XXXXX'">g</span><span style="XXXX-size:10pt;font-family:'XXXXX New Roman'">o</span><span style="font-style:italic;XXXX-size:12pt;XXXX-family:'XXXXX XXX XXXXX'">f</span><span style="XXXX-size:12pt;XXXX-XXXXXX:'Times XXX XXXXX'">)(</span><span style="font-style:XXXXXX;XXXX-XXXX:XXXX;font-family:'XXXXX New XXXXX'">x</span><span style="font-XXXX:XXXX;XXXX-XXXXXX:'XXXXX XXX XXXXX'">)</span><span style="font-style:italic;XXXX-XXXX:12pt;font-XXXXXX:'Times XXX Roman'">[4 XXXXX]</span><span></span><span style="XXXX-style:italic;XXXX-XXXX:12pt;XXXX-XXXXXX:'Times New Roman'"> f</span><span style="font-style:italic;font-XXXX:XXXX;XXXX-family:'XXXXX XXX XXXXX';vertical-XXXXX:super">-X</span><span style="font-size:XXXX;font-family:'Times XXX XXXXX'">(</span><span style="XXXX-style:XXXXXX;XXXX-size:12pt;font-XXXXXX:'Times New XXXXX'">x</span><span style="font-size:12pt;XXXX-XXXXXX:'XXXXX New XXXXX'">)</span><span style="font-style:italic;XXXX-XXXX:XXXX;XXXX-family:'XXXXX New XXXXX'">[3 XXXXX]</span><span></span><span style="font-style:XXXXXX;XXXX-size:XXXX;font-XXXXXX:'Times New XXXXX'"> g</span><span style="font-style:XXXXXX;font-XXXX:XXXX;font-XXXXXX:'Times XXX XXXXX';XXXXXXXX-XXXXX:XXXXX">-1</span><span style="font-size:12pt;font-family:'XXXXX XXX Roman'">(10)</span><span style="font-style:italic;XXXX-size:XXXX;XXXX-family:'Times XXX XXXXX'">[2 XXXXX]</span><span></span><span style="XXXX-size:12pt;font-family:'Times New Roman'"> (</span><span style="font-style:XXXXXX;XXXX-size:12pt;XXXX-XXXXXX:'Times New XXXXX'">f</span><span style="XXXX-style:italic;font-XXXX:12pt;XXXX-family:'XXXXX XXX XXXXX';vertical-align:XXXXX">-X</span><span style="XXXX-XXXX:12pt;font-family:'Times New XXXXX'">o</span><span style="XXXX-style:italic;font-size:12pt;XXXX-XXXXXX:'XXXXX XXX Roman'">g</span><span style="XXXX-XXXX:XXXX;font-family:'Times XXX Roman'">)(</span><span style="XXXX-style:italic;font-size:XXXX;font-family:'XXXXX XXX XXXXX'">x</span><span style="font-size:12pt;font-XXXXXX:'Times XXX Roman'">)</span><span style="font-style:XXXXXX;XXXX-XXXX:12pt;XXXX-family:'XXXXX New Roman'">[X XXXXX]</span><span></span><span style="font-XXXX:XXXX;font-XXXXXX:'XXXXX New XXXXX'"> (</span><span style="font-style:XXXXXX;XXXX-size:12pt;XXXX-family:'Times XXX Roman'">g</span><span style="XXXX-size:10pt;font-family:'Times XXX Roman'">o</span><span style="XXXX-style:XXXXXX;font-XXXX:12pt;XXXX-XXXXXX:'Times New XXXXX'">f</span><span style="XXXX-XXXX:12pt;XXXX-family:'Times XXX Roman'">)</span><span style="font-style:XXXXXX;font-XXXX:12pt;XXXX-XXXXXX:'Times New Roman';XXXXXXXX-XXXXX:super"> -X</span><span style="XXXX-XXXX:XXXX;XXXX-XXXXXX:'Times XXX XXXXX'">(</span><span style="XXXX-style:italic;font-size:XXXX;XXXX-family:'XXXXX XXX Roman'">x</span><span style="XXXX-size:XXXX;XXXX-family:'Times New Roman'">)</span><span style="XXXX-style:XXXXXX;XXXX-size:12pt;font-XXXXXX:'XXXXX New XXXXX'">[X XXXXX]</span><span></span><span style="font-family:'XXXXX XXX XXXXX'"> (</span><span style="XXXX-style:italic;font-family:'Times New Roman'">f</span><span style="font-size:XXXX;font-family:'Times XXX Roman'">o</span><span style="XXXX-style:italic;font-XXXXXX:'Times XXX Roman'">f</span><span style="font-XXXXXX:'XXXXX New XXXXX'">)(</span><span style="font-style:XXXXXX;font-family:'Times XXX XXXXX'">x</span><span style="XXXX-XXXXXX:'XXXXX New XXXXX'">)</span> <p> XXXXXXXX: </p> <span></span><span style="font-XXXXXX:bold">Calculate</span><span style="font-weight:XXXX;XXXX-size:12pt;XXXX-family:'XXXXX New XXXXX'">(</span><span style="XXXX-XXXXXX:bold;XXXX-style:italic;font-XXXX:XXXX;XXXX-family:'Times XXX XXXXX'">f</span><span style="XXXX-XXXXXX:bold;font-XXXX:XXXX;font-XXXXXX:'Times XXX XXXXX'">o</span><span style="font-XXXXXX:bold;XXXX-style:XXXXXX;XXXX-XXXX:XXXX;font-XXXXXX:'XXXXX New Roman'">g</span><span style="font-weight:XXXX;font-XXXX:12pt;XXXX-XXXXXX:'XXXXX XXX Roman'">)(</span><span style="font-XXXXXX:XXXX;XXXX-style:XXXXXX;font-XXXX:12pt;font-XXXXXX:'Times XXX Roman'">x</span><span style="font-weight:bold;font-XXXX:XXXX;font-XXXXXX:'Times XXX XXXXX'">) XXX (</span><span style="font-XXXXXX:XXXX;font-style:XXXXXX;font-size:12pt;font-XXXXXX:'XXXXX New XXXXX'">g</span><span style="font-weight:XXXX;font-XXXX:10pt;font-XXXXXX:'XXXXX New Roman'">o</span><span style="font-weight:XXXX;XXXX-style:italic;font-size:XXXX;XXXX-family:'Times XXX Roman'">f</span><span style="XXXX-weight:bold;font-XXXX:XXXX;font-family:'Times XXX XXXXX'">)(</span><span style="font-weight:XXXX;font-style:XXXXXX;XXXX-size:XXXX;XXXX-XXXXXX:'Times XXX Roman'">x</span><span style="XXXX-XXXXXX:XXXX;XXXX-size:XXXX;XXXX-family:'XXXXX XXX Roman'">)</span> <p> <span style="XXXX-family:'Times New XXXXX'">XXXXXXXX:</span> </p> <p awml:style="List Paragraph"> </p> <p awml:style="List XXXXXXXXX"> </p> <p awml:style="XXXX Paragraph"> </p> <p awml:style="List Paragraph"> </p> <p awml:style="XXXX XXXXXXXXX"> <span style="XXXX-XXXX:XXXX">XXX</span> </p> <p awml:style="XXXX XXXXXXXXX"> </p> <p awml:style="List XXXXXXXXX"> </p> <p awml:style="List XXXXXXXXX"> </p> <p awml:style="List XXXXXXXXX"> </p> <span></span><span style="XXXX-weight:XXXX;XXXX-XXXX:12pt;font-family:'Times New XXXXX'">XXXXXXXXX</span><span style="font-XXXXXX:XXXX;XXXX-style:XXXXXX;XXXX-size:12pt;XXXX-family:'Times XXX XXXXX'">f</span><span style="font-XXXXXX:XXXX;font-style:italic;XXXX-XXXX:XXXX;font-family:'Times New XXXXX';vertical-XXXXX:XXXXX">-1</span><span style="font-XXXXXX:bold;font-size:XXXX;XXXX-family:'Times XXX XXXXX'">(</span><span style="XXXX-weight:bold;XXXX-style:italic;font-XXXX:XXXX;XXXX-XXXXXX:'Times XXX XXXXX'">x</span><span style="font-XXXXXX:bold;XXXX-XXXX:12pt;XXXX-family:'Times XXX XXXXX'">)</span> <p> Solution: </p> <p> XXX,, </p> <p> </p> <p> </p> <p> </p> <p style="margin-left:XX.000000pt"> Using XX. XXXXXX (X) </p> <p style="XXXXXX-XXXX:XX.XXXXXXXX"> </p> <p style="XXXXXX-XXXX:18.XXXXXXXX"> Now, X XXXXXXX XX X </p> <p style="margin-XXXX:XX.XXXXXXXX"> </p> <span></span><span style="XXXX-weight:bold;font-XXXXXX:'XXXXX New Roman'">XXXXXXXXX</span><span style="XXXX-weight:bold;font-style:XXXXXX;XXXX-XXXXXX:'Times XXX Roman'">g</span><span style="XXXX-weight:XXXX;font-style:XXXXXX;font-XXXXXX:'XXXXX New XXXXX';XXXXXXXX-align:XXXXX">-X</span><span style="XXXX-XXXXXX:bold;font-family:'Times XXX Roman'">(XX)</span> <p> Solution: </p> <p> XXXXX, XX XXXX XXXX to find </p> <p> XXX, </p> <p> </p> <p> </p> <p> </p> <p> </p> <p> Using XX. number (1) </p> <p> </p> <p style="margin-XXXX:XX.000000pt"> XXX, X XXXXXXXX XX X </p> <p> </p> <p> XXX </p> <p> </p> <p> </p> <span></span><span style="XXXX-XXXXXX:XXXX;XXXX-size:12pt;font-XXXXXX:'XXXXX XXX Roman'">Calculate (</span><span style="font-XXXXXX:bold;XXXX-style:XXXXXX;font-size:12pt;font-XXXXXX:'XXXXX New XXXXX'">f</span><span style="XXXX-XXXXXX:XXXX;font-style:italic;font-size:XXXX;font-XXXXXX:'XXXXX XXX Roman';vertical-align:XXXXX">-1</span><span style="font-XXXXXX:XXXX;font-XXXX:XXXX;font-XXXXXX:'XXXXX New Roman'">o</span><span style="XXXX-weight:XXXX;font-style:italic;font-size:12pt;font-family:'Times XXX Roman'">g</span><span style="font-XXXXXX:XXXX;font-size:XXXX;font-XXXXXX:'XXXXX New Roman'">) (</span><span style="font-weight:bold;font-style:italic;font-size:12pt;XXXX-XXXXXX:'XXXXX New XXXXX'">x</span><span style="XXXX-XXXXXX:XXXX;XXXX-size:XXXX;XXXX-XXXXXX:'Times New XXXXX'">)</span> <p style="margin-left:XX.XXXXXXXX"> XXXXXXXX: </p> <p style="margin-XXXX:18.000000pt"> XX XX XXXXX in<span style="font-weight:bold;font-style:italic;XXXX-XXXX:14pt">b)</span> XXXX, </p> <p style="margin-XXXX:18.000000pt"> </p> <p style="XXXXXX-left:6.000000pt"> </p> <p style="XXXXXX-XXXX:6.XXXXXXXX"> <span style="XXXX-XXXXXX:'XXXXX New Roman'">XX, </span> </p> <p style="margin-left:X.000000pt"> <span style="font-family:'Times XXX Roman'">Thus,</span> </p> <span></span><span style="font-XXXXXX:XXXX;XXXX-XXXX:12pt;XXXX-family:'Times New Roman'">Calculate (</span><span style="font-weight:XXXX;XXXX-style:XXXXXX;font-XXXX:12pt;XXXX-family:'Times New XXXXX'">g</span><span style="font-weight:bold;XXXX-XXXX:10pt;font-family:'Times New XXXXX'">o</span><span style="font-weight:XXXX;XXXX-style:XXXXXX;XXXX-XXXX:XXXX;XXXX-XXXXXX:'Times XXX Roman'">f</span><span style="font-weight:bold;font-XXXX:XXXX;XXXX-family:'Times XXX Roman'">)</span><span style="XXXX-XXXXXX:bold;font-style:XXXXXX;XXXX-XXXX:XXXX;font-XXXXXX:'Times XXX XXXXX';vertical-XXXXX:XXXXX"> -X</span><span style="font-weight:bold;font-size:XXXX;XXXX-family:'XXXXX XXX XXXXX'">(</span><span style="font-XXXXXX:bold;font-style:italic;font-size:XXXX;font-family:'Times New Roman'">x</span><span style="XXXX-weight:bold;font-XXXX:12pt;font-XXXXXX:'XXXXX XXX Roman'">)</span> <p> XXXXXXXX: </p> <p> First, XX XXXX need XX XXXX </p> <p> <span style="font-weight:bold">As we XXXXXX already in</span><span style="XXXX-XXXXXX:bold;XXXX-XXXX:14pt">a)</span><span style="XXXX-XXXXXX:bold"> XXXX that is</span>, </p> <p awml:style="XXXX Paragraph"> </p> <p awml:style="XXXX XXXXXXXXX"> <span style="font-size:12pt">Let</span> </p> <p awml:style="List XXXXXXXXX"> </p> <p awml:style="List XXXXXXXXX"> <span style="font-XXXX:XXXX">Now,</span> </p> <p> </p> <p> </p> <p> <span style="XXXX-XXXXXX:'Calibri'">Using XX. XXXXXX (X)</span> </p> <p> </p> <p> <span style="XXXX-family:'Calibri'">y XXXXXXXX by x,</span> </p> <p> </p> <span></span><span style="font-weight:XXXX;font-family:'XXXXX XXX XXXXX'">XXXXXXXXX</span><span style="XXXX-XXXXXX:bold;font-family:'XXXXX New XXXXX'">(</span><span style="XXXX-XXXXXX:XXXX;font-style:italic;font-XXXXXX:'Times New XXXXX'">f</span><span style="font-XXXXXX:bold;XXXX-size:XXXX;XXXX-XXXXXX:'XXXXX New XXXXX'">o</span><span style="font-XXXXXX:XXXX;font-style:XXXXXX;font-family:'XXXXX XXX Roman'">f</span><span style="font-weight:bold;XXXX-family:'XXXXX New Roman'">)</span><span style="XXXX-XXXXXX:XXXX;XXXX-family:'XXXXX New XXXXX'"></span><span style="XXXX-XXXXXX:bold;font-XXXXXX:'Times New XXXXX'">(</span><span style="XXXX-XXXXXX:bold;XXXX-style:XXXXXX;XXXX-XXXXXX:'Times XXX Roman'">x</span><span style="XXXX-XXXXXX:XXXX;XXXX-family:'Times XXX XXXXX'">)</span> <p style="margin-XXXX:18.000000pt"> <span style="font-XXXXXX:'XXXXX New Roman'">Solution:</span> </p> <p style="XXXXXX-left:18.000000pt"> </p> <p style="margin-XXXX:18.XXXXXXXX"> </p> <p style="XXXXXX-left:18.XXXXXXXX"> </p> <p style="margin-left:XX.XXXXXXXX"> <span style="XXXX-XXXXXX:'Times XXX Roman'">Thus,</span> </p> <p style="XXXXXX-left:XX.000000pt"> </p> <span></span><span style="font-size:12pt;XXXX-XXXXXX:'XXXXX New Roman'">XXX XXXXX of XXX XXXXXXXX</span><span style="XXXX-style:italic;XXXX-size:XXXX;font-family:'Times XXX Roman'">f</span><span style="XXXX-XXXX:12pt;font-family:'XXXXX XXX Roman'">(</span><span style="XXXX-style:XXXXXX;font-size:XXXX;font-family:'Times XXX Roman'">x</span><span style="XXXX-XXXX:12pt;font-family:'XXXXX New XXXXX'">) XX the segment XX a line, XXXX endpoints</span><span style="font-XXXXXX:XXXX;font-style:italic;font-XXXX:12pt;font-family:'XXXXX XXX XXXXX'">X</span><span style="XXXX-size:12pt;font-family:'Times New XXXXX'">(-1,6) and</span><span style="font-weight:XXXX;font-style:italic;XXXX-size:12pt;font-family:'Times New Roman'">B</span><span style="font-size:XXXX;font-XXXXXX:'Times XXX Roman'">(X,-X), XX shown below.</span> <p class="list_paragraph" style="XXXX-XXXXX:XXXXXX;margin-XXXX:XX.000000pt" awml:style="XXXX XXXXXXXXX"> Images Not Shown</p> <p class="XXXXXXXXXXXXXX" style="XXXX-align:XXXXXXX" awml:style="List XXXXXXXXX"> <span style="font-XXXX:12pt;font-family:'Times New Roman'">XXXXX down</span> </p> <span></span><span style="font-XXXX:XXXX;font-XXXXXX:'Times New Roman'"> The</span><span style="XXXX-style:italic;font-size:XXXX;XXXX-XXXXXX:'Times New Roman'">y</span><span style="XXXX-size:XXXX;font-XXXXXX:'XXXXX XXX Roman'">-XXXXXXXXX and the root of the function.</span><span></span><span style="XXXX-XXXX:12pt;XXXX-XXXXXX:'Times New XXXXX'">The XXXXXX</span><span style="font-style:italic;XXXX-XXXX:12pt;font-family:'XXXXX XXX XXXXX'">f</span><span style="XXXX-size:12pt;font-XXXXXX:'XXXXX New XXXXX'">(1.X) and</span><span style="font-style:italic;font-size:12pt;font-family:'XXXXX New Roman'">f</span><span style="XXXX-size:12pt;XXXX-family:'Times New Roman';XXXXXXXX-XXXXX:super">-1</span><span style="XXXX-size:XXXX;font-family:'XXXXX XXX Roman'">(2)</span><span></span><span style="XXXX-XXXX:12pt;XXXX-XXXXXX:'Times New Roman'"> The domain XXX the XXXXX XX XXX XXXXXXXX</span><span style="XXXX-style:XXXXXX;font-XXXX:XXXX;font-XXXXXX:'XXXXX New XXXXX'">f</span><span style="XXXX-size:12pt;font-XXXXXX:'Times XXX XXXXX'"></span> <p class="XXXXXXXXXXXXXX" style="XXXX-align:justify;XXXXXX-bottom:0.000000pt;margin-XXX:6.000000pt" awml:style="XXXX Paragraph"> <span style="XXXX-XXXX:XXXX;XXXX-family:'Times New XXXXX'">For the XXXXXXX function</span><span style="font-style:XXXXXX;font-size:XXXX;font-XXXXXX:'Times New Roman'">f</span><span style="font-XXXX:12pt;XXXX-XXXXXX:'XXXXX New XXXXX';vertical-align:super">-1</span><span style="XXXX-size:XXXX;font-family:'XXXXX New Roman'">, the corresponding point XX</span><span style="XXXX-weight:bold;XXXX-style:italic;font-XXXX:12pt;font-family:'XXXXX XXX Roman'">A</span><span style="font-XXXX:XXXX;font-XXXXXX:'Times New Roman';vertical-align:super"> XX</span><span style="font-XXXX:XXXX;font-XXXXXX:'Times New XXXXX'"> the XXXXX</span><span style="XXXX-XXXXXX:bold;XXXX-style:italic;XXXX-XXXX:12pt;XXXX-XXXXXX:'XXXXX XXX Roman'">A</span><span style="font-XXXXXX:bold;XXXX-XXXX:12pt;XXXX-XXXXXX:'XXXXX New XXXXX'">΄</span><span style="font-weight:XXXX;font-XXXX:XXXX;XXXX-XXXXXX:'Times New Roman'"> (6, -X)</span> </p> <span></span><span style="XXXX-size:12pt;XXXX-family:'XXXXX XXX XXXXX'"> XXXXX down the coordinates XX</span><span style="font-weight:XXXX;XXXX-style:XXXXXX;font-size:XXXX;XXXX-XXXXXX:'XXXXX XXX XXXXX'">X</span><span style="font-weight:XXXX;XXXX-style:italic;font-size:12pt;XXXX-family:'Times XXX Roman'">΄</span><span style="font-XXXX:12pt;font-XXXXXX:'Times New Roman'">, the</span><span style="XXXX-style:XXXXXX;font-XXXX:XXXX;XXXX-XXXXXX:'Times New Roman'">XXXXXXXXXXXXX</span><span style="XXXX-XXXX:12pt;font-family:'XXXXX New XXXXX'"> XXXXX of</span><span style="XXXX-style:XXXXXX;font-XXXX:XXXX;font-family:'Times XXX Roman'"></span><span style="XXXX-XXXXXX:XXXX;XXXX-style:italic;XXXX-XXXX:12pt;font-XXXXXX:'XXXXX New Roman'">X</span><span style="font-XXXX:12pt;XXXX-family:'XXXXX New Roman'"></span><span></span><span style="XXXX-XXXX:12pt;XXXX-XXXXXX:'XXXXX XXX Roman'"> XXXXX, sketch XXX graph of</span><span style="XXXX-style:italic;font-XXXX:XXXX;font-XXXXXX:'XXXXX XXX XXXXX'"> f</span><span style="XXXX-size:12pt;XXXX-XXXXXX:'Times New XXXXX';vertical-XXXXX:XXXXX">-1</span><span style="XXXX-size:12pt;XXXX-XXXXXX:'Times New Roman'">XX XXX same XXXX XXXXX.</span> <p style="XXXX-XXXXX:justify"> <span style="XXXX-XXXXXX:XXXX;XXXX-family:'XXXXX New Roman'">Solution (a): XXX</span><span style="font-weight:XXXX;font-style:italic;XXXX-XXXXXX:'XXXXX New XXXXX'">y</span><span style="XXXX-XXXXXX:XXXX;XXXX-XXXXXX:'Times New Roman'">-intercept and XXX XXXX of the function.</span><span style="XXXX-XXXXXX:'XXXXX XXX Roman'"></span> </p> <p style="XXXX-XXXXX:XXXXXXX"> <span style="XXXX-XXXXXX:'XXXXX XXX Roman'">From the XXXXX XXXXX we XXX clearly find the y-XXXXXXXXX i.e. (X, 4) XXX XXX XXXX of XXX XXXXXXXX or x-XXXXXXXXX XX (X,X).</span> </p> <p style="XXXX-XXXXX:XXXXXXX"> <span style="XXXX-family:'Times XXX XXXXX'">XX XXXXXXXXX XXX given XXXXXX, XX XXX find XXX y-XXXXXXXXX XXX XXXX of the function.</span> </p> <p XXXXX="XXXXXXXXXXXXXX" style="text-XXXXX:justify;margin-left:XX.000000pt" awml:style="List XXXXXXXXX"> <span style="XXXX-XXXXXX:'Times New XXXXX';XXXXXXXXXX:#ffffff">XXXXX, we will find XXX XXXXXXXX XXX a line that XXXXXX XXXXXXX XXX XXX points:</span> </p> <p XXXXX="XXXXXXXXXXXXXX" style="XXXX-XXXXX:justify;XXXXXX-left:XX.XXXXXXXX" awml:style="List XXXXXXXXX"> <span style="XXXX-XXXXXX:'Times New XXXXX'">(-X,6) XXX (3,-2).</span> </p> <p XXXXX="list_paragraph" style="XXXX-align:XXXXXXX;XXXXXX-XXXX:XX.000000pt" awml:style="List Paragraph"> </p> <p XXXXX="XXXXXXXXXXXXXX" style="XXXX-XXXXX:XXXXXXX;XXXXXX-XXXX:18.XXXXXXXX" awml:style="XXXX XXXXXXXXX"> <span style="font-size:12pt;font-XXXXXX:'Times XXX XXXXX'">XXXXX m XX XXX slope, and c XX XXX y-intercept.</span> </p> <p XXXXX="list_paragraph" style="XXXX-align:justify;margin-left:XX.XXXXXXXX" awml:style="List Paragraph"> </p> <p class="XXXXXXXXXXXXXX" style="text-align:XXXXXXX;margin-left:XX.000000pt" awml:style="List Paragraph"> </p> <p class="XXXXXXXXXXXXXX" style="XXXX-XXXXX:justify;XXXXXX-XXXX:18.XXXXXXXX" awml:style="List XXXXXXXXX"> </p> <p XXXXX="list_paragraph" style="text-XXXXX:XXXXXXX;XXXXXX-XXXX:XX.XXXXXXXX" awml:style="XXXX XXXXXXXXX"> <span style="XXXX-size:XXXX;XXXX-XXXXXX:'Times New XXXXX'">Now eq. XX the line</span> </p> <p class="XXXXXXXXXXXXXX" style="XXXX-align:justify;XXXXXX-left:XX.000000pt" awml:style="List XXXXXXXXX"> </p> <p class="list_paragraph" style="XXXX-align:justify;margin-XXXX:XX.000000pt" awml:style="XXXX Paragraph"> </p> <p XXXXX="XXXXXXXXXXXXXX" style="XXXX-align:XXXXXXX;margin-left:18.XXXXXXXX" awml:style="XXXX XXXXXXXXX"> <span style="font-XXXX:12pt;font-family:'Times XXX XXXXX'">XXX y-intercept, XXX x=0</span> </p> <p XXXXX="list_paragraph" style="XXXX-XXXXX:XXXXXXX;margin-XXXX:18.000000pt" awml:style="List XXXXXXXXX"> </p> <p XXXXX="XXXXXXXXXXXXXX" style="XXXX-XXXXX:XXXXXXX;margin-XXXX:XX.000000pt" awml:style="List Paragraph"> <span style="font-size:12pt;font-family:'Times New Roman'">XX</span> </p> <p class="XXXXXXXXXXXXXX" style="XXXX-align:justify;margin-left:XX.000000pt" awml:style="List XXXXXXXXX"> <span style="XXXX-size:12pt;XXXX-XXXXXX:'XXXXX New Roman'">XXX XXXX XX XXX XXXXXXXX is,</span> </p> <p class="list_paragraph" style="XXXX-align:justify;XXXXXX-XXXX:XX.XXXXXXXX" awml:style="XXXX Paragraph"> </p> <p XXXXX="list_paragraph" style="XXXX-XXXXX:justify;XXXXXX-XXXX:18.000000pt" awml:style="List Paragraph"> </p> <p XXXXX="XXXXXXXXXXXXXX" style="text-align:justify;margin-left:XX.000000pt" awml:style="List XXXXXXXXX"> <span style="font-XXXX:XXXX;font-XXXXXX:'XXXXX New XXXXX'">So,</span> </p> <p class="list_paragraph" style="text-XXXXX:justify;margin-XXXX:18.XXXXXXXX" awml:style="XXXX XXXXXXXXX"> </p> <p XXXXX="XXXXXXXXXXXXXX" style="XXXX-XXXXX:justify;XXXXXX-XXXX:XX.XXXXXXXX" awml:style="List XXXXXXXXX"> <span style="XXXX-weight:bold;XXXX-XXXX:XXXX;font-family:'XXXXX XXX XXXXX'">Solution (b): XXXXX down XXX XXXXXX</span><span style="XXXX-weight:XXXX;font-style:italic;XXXX-XXXX:XXXX;XXXX-family:'Times New XXXXX'">f</span><span style="XXXX-XXXXXX:XXXX;font-XXXX:XXXX;font-family:'Times XXX XXXXX'">(X.5) and</span><span style="font-XXXXXX:XXXX;XXXX-style:italic;font-XXXX:XXXX;XXXX-XXXXXX:'Times New XXXXX'">f</span><span style="font-weight:XXXX;XXXX-XXXX:12pt;XXXX-family:'Times New Roman';XXXXXXXX-XXXXX:XXXXX">-1</span><span style="XXXX-XXXXXX:XXXX;font-XXXX:12pt;font-family:'Times New XXXXX'">(X)</span> </p> <p class="list_paragraph" style="text-XXXXX:justify;XXXXXX-left:18.XXXXXXXX" awml:style="XXXX XXXXXXXXX"> <span style="font-XXXX:XXXX;XXXX-family:'Times XXX Roman'">XX can see from above in XXXX (a)</span> </p> <p XXXXX="list_paragraph" style="text-align:XXXXXXX;margin-XXXX:XX.000000pt" awml:style="List XXXXXXXXX"> </p> <p XXXXX="list_paragraph" style="XXXX-align:XXXXXXX;XXXXXX-left:XX.000000pt" awml:style="XXXX XXXXXXXXX"> </p> <p XXXXX="XXXXXXXXXXXXXX" style="text-XXXXX:justify;margin-XXXX:XX.000000pt" awml:style="List Paragraph"> </p> <p class="XXXXXXXXXXXXXX" style="text-align:XXXXXXX;margin-XXXX:XX.000000pt" awml:style="List Paragraph"> <span style="XXXX-size:12pt;font-family:'Times XXX XXXXX'">XXXX, we can see the XXXXX of f(x) at</span><span style="XXXX-size:XXXX;font-family:'Times New XXXXX'"> from XXX XXXXX graph i.e</span> </p> <p class="list_paragraph" style="XXXX-XXXXX:justify;XXXXXX-left:XX.XXXXXXXX" awml:style="List XXXXXXXXX"> </p> <p style="XXXX-XXXXX:justify"> <span style="font-family:'Times New Roman'">Now XXX</span><span style="XXXX-XXXXXX:XXXX;font-style:italic;font-family:'Times XXX XXXXX'">f</span><span style="font-weight:XXXX;font-XXXXXX:'Times XXX Roman';vertical-align:super">-1</span><span style="font-weight:XXXX;XXXX-family:'XXXXX XXX Roman'">(X),</span><span style="XXXX-family:'Times New Roman'">using XXX given XXXXX</span> </p> <p style="XXXX-XXXXX:XXXXXXX"> <span style="font-family:'Times New Roman'">As</span> </p> <p style="text-XXXXX:justify"> </p> <p style="XXXX-XXXXX:justify"> <span style="XXXX-family:'Times New Roman'">As</span> </p> <p XXXXX="XXXXXXXXXXXXXX" style="XXXX-XXXXX:XXXXXXX;XXXXXX-left:18.000000pt" awml:style="List Paragraph"> </p> <p class="list_paragraph" style="text-align:XXXXXXX;margin-XXXX:XX.XXXXXXXX" awml:style="XXXX Paragraph"> <span style="font-XXXX:XXXX;font-family:'XXXXX New Roman'">XX,</span> </p> <p XXXXX="list_paragraph" style="XXXX-align:XXXXXXX;XXXXXX-XXXX:XX.000000pt" awml:style="List XXXXXXXXX"> </p> <p style="XXXX-XXXXX:XXXXXXX"> <span style="XXXX-XXXXXX:'XXXXX New Roman'">c) Write down XXX XXXXXX and range of XXX function f</span> </p> <p style="XXXX-align:justify"> <span style="XXXX-XXXXXX:'Times XXX Roman'">Solution:</span> </p> <p style="text-XXXXX:justify"> </p> <p style="XXXX-align:justify"> </p> <p style="text-XXXXX:XXXXXXX"> <span style="font-family:'XXXXX XXX XXXXX';color:#000000">Overall</span><span style="font-family:'XXXXX New Roman';XXXXX:#000000">&XXX;</span> </p> <span></span><span style="font-family:'Times New XXXXX'">XXXXX XXXX XXX coordinates of</span><span style="XXXX-weight:bold;font-style:italic;XXXX-XXXXXX:'XXXXX New XXXXX'">B΄</span><span style="XXXX-XXXXXX:'XXXXX XXX Roman'">, the</span><span style="XXXX-style:italic;font-family:'Times New Roman'"></span><span style="XXXX-XXXXXX:'XXXXX New Roman'">corresponding point XX</span><span style="XXXX-style:XXXXXX;font-XXXXXX:'Times XXX XXXXX'"></span><span style="XXXX-XXXXXX:XXXX;font-style:XXXXXX;XXXX-XXXXXX:'XXXXX XXX XXXXX'">B</span><span style="font-weight:bold;XXXX-XXXXXX:'XXXXX XXX XXXXX'">(3,-X)</span> <p style="XXXX-align:XXXXXXX"> <span style="font-family:'Times XXX XXXXX'">Solution:</span> </p> <p style="text-XXXXX:XXXXXXX"> <span style="XXXX-XXXXXX:'Times XXX Roman'">coordinates of</span><span style="font-weight:bold;XXXX-family:'XXXXX New Roman'">)</span><span style="font-XXXXXX:'XXXXX New XXXXX'"></span></p> <p style="text-XXXXX:justify"> </p> <p style="text-align:justify"> </p> <p style="XXXX-XXXXX:XXXXXXX"> </p> <p style="XXXX-XXXXX:XXXXXXX"> </p> <p style="text-align:XXXXXXX"> </p> <span></span><span style="XXXX-XXXX:XXXX;XXXX-family:'XXXXX New Roman'">Hence, sketch XXX XXXXX XX</span><span style="XXXX-style:XXXXXX;font-XXXX:XXXX;XXXX-family:'XXXXX XXX XXXXX'"> f</span><span style="font-size:12pt;XXXX-family:'Times XXX XXXXX';XXXXXXXX-align:super">-X</span><span style="font-XXXX:12pt;XXXX-XXXXXX:'XXXXX New XXXXX'">XX XXX XXXX XXXX above.</span> <p class="XXXXXXXXXXXXXX" style="text-align:justify" awml:style="XXXX Paragraph"> <span style="font-size:XXXX;XXXX-XXXXXX:'XXXXX XXX Roman'">Solution:</span> </p> <p class="list_paragraph" style="XXXX-align:XXXXXXX" awml:style="List XXXXXXXXX"> <span style="font-XXXX:XXXX;font-family:'Times New Roman'">Points for</span><span style="XXXX-size:12pt;XXXX-family:'Times New Roman'">.</span> </p> <p class="XXXXXXXXXXXXXX" style="text-align:XXXXXXX" awml:style="List Paragraph"> </p> <p class="XXXXXXXXXXXXXX" style="XXXX-XXXXX:justify" awml:style="XXXX Paragraph"> </p> <p style="XXXX-XXXXX:XXXXXXX"> </p> <p style="text-align:justify"> </p> <p XXXXX="list_paragraph" style="text-align:XXXXXXX;XXXXXX-XXXX:XX.000000pt" awml:style="List Paragraph"> </p> <p class="list_paragraph" style="XXXX-align:XXXXXXX;margin-XXXX:XX.000000pt" awml:style="XXXX XXXXXXXXX"> </p> <p XXXXX="XXXXXXXXXXXXXX" style="text-XXXXX:XXXXXXX;XXXXXX-XXXX:18.000000pt" awml:style="List Paragraph"> </p> <p class="XXXXXXXXXXXXXX" style="XXXX-align:justify;margin-left:18.XXXXXXXX" awml:style="XXXX Paragraph"> </p> <p XXXXX="list_paragraph" style="XXXX-align:XXXXXXX;margin-XXXX:18.000000pt" awml:style="XXXX XXXXXXXXX"> </p> <p XXXXX="XXXXXXXXXXXXXX" style="XXXX-XXXXX:justify;XXXXXX-XXXX:XX.XXXXXXXX" awml:style="List Paragraph"> </p> </div> </body></XXXX>">
