Question

Hello I just need the answer for “What is the inverse for the equation y=x^2+16”

Answer 1

Given:

The given equation is

$y=x^2+16$

Required:

We need to find the inverse for the equation.

Explanation:

$\text{ Let y=f\lparen x\rparen and }x=f^{-1}(y)\text{ and substitute }x=f^{-1}(y)\text{ in the given equation.}$$y=(f^{-1}(y))^2+16$

Substract 16 from both sides of the equation.

$y-16=(f^{-1}(y))^2+16-16$$y-16=(f^{-1}(y))^2$

Take square root on both sides of the equation.

$\pm\sqrt{(y-16)}=f^{-1}(y)$$f^{-1}(y)=\pm\sqrt{(y-16)}$

Replace y=x in the equation.

$f^{-1}(x)=\pm\sqrt{x-16}$

Final answer:

$f^{-1}(x)=\pm\sqrt{x-16}$