Decide whether or not the functions are inverses

Question

Decide whether or not the functions are inverses of each other.f(x) = (x - 3)2, x ≥ 3

Answer

Answer

Good morning, andreacruz! I’m new to School Solver and this is my first time answering a question, so please bear with me if I make any mistakes.

You find the inverse of a function by changing all of its 𝑦’s to 𝑥’s (and vice versa). Then, you rearrange the new equation so as to solve for 𝑦, thereby generating the inverse of the original function. In the case of your first function, 𝑓(𝑥) = (𝑥 – 3)2, it depends on whether you meant to multiply “(𝑥 – 3)” by two, 2(𝑥 – 3), or square it, (𝑥 – 3)². Either way, here’s the solution for both cases:   
 
  
𝑓(𝑥) = 2(𝑥 – 3)
  
𝑦 = 2(𝑥 – 3)
  
𝑥 = 2(𝑦 – 3)
  
𝑥 / 2 = 𝑦 – 3
  
(𝑥 / 2) + 3 = 𝑦
(𝑥 / 2) + 3 = 𝑓⁻¹(𝑥) (the inverse of function "𝑓(𝑥)")
 
  
𝑓(𝑥) = (𝑥 – 3)²
  
𝑦 = (𝑥 – 3)²
  
𝑥 = (𝑦 – 3)²
  
± √𝑥 = 𝑦 – 3
  
3 ± √𝑥 = 𝑦
3 ± √𝑥 = 𝑓⁻¹(𝑥)

The inverse of 𝑥 ≥ 3 is, in turn, simply 𝑦 ≥ 3.

Since the first expression is an EQUATION (=), whereas the second one is an INEQUALITY (≥), the two expressions definitely cannot be the inverses of one another. 

I’m not sure if most students come here to learn how to do things, or to get answers to homework. If you’re interested in learning how to find the inverses of functions, the following video tutorial might help:

Best of luck!

Answer

let f(x) = 2 * (x - 3)f(3) = 2 * ((3) - 3)f(3) = 2 * (0)f(3) = 0if f(x) = x in this situation we can conclude that the functions are inverseswe would expect f(3) to equal 3, therefor, the functions are NOT inverses.

Category:	Mathematics
Offered Price:	$75.00
Due Date:	27 August 2017, 09:08
Added:	27 August 2017, 17:26

Price:	0.50
Added:	27 August 2017, 18:28
Buyers:	No Buyers Yet

Price:	75.00
Added:	28 August 2017, 08:22
Words:	259 words
Buyers:	No Buyers Yet

Price:	1.00
Added:	28 August 2017, 20:50
Words:	45 words
Buyers:	No Buyers Yet

Decide whether or not the functions are inverses

Secure Payment

We let the professionals process your money

Secure Payment

We let the professionals process your money

Secure Payment

We let the professionals process your money

Have a similar question?