Let f(x) = x^2 - 16. Find f-1(x).

Question

Let f(x) = x^2 − 16. Find f−1(x).

Answer 1

f(x) = x² - 16

 

To find f^-1(x) or f-inverse...

1.  replace f(x) with y ...          y = x²-16

2.  switch x and y variables...  x = y²-16

3.  solve for y

       

     x = y²-16

     y² = x+16

     y = √(x+16)

 

4.  replace 'y'  with  f^-1(x)

     f^-1(x) = √(x+16)

 

Answer 2

I'm reading that as the inverse function of x.

  x^2 - 16

 

if you subtract 16, from x^2 ,  then you have to add 16 to get back to x^2 (from which you would then do the subtraction to complete f(x), let us call f(x) y, then

 if we have  y + 16 then we take the square root to get back to original x

  _________________

|/  y` + 16

 

so x =9 f(x) == 81 -16 ==65 :: y=65

y = 65: add 16, get 81, take the s root, that is 9, the original input 

ta da 

:)

 

Or what andrew said.  no answers were posted  when I started writing this...

well done andrew.