Chapter 3.7, Problem 49E

To determine

To find: the inverse of the given equation.

Answer to Problem 49E

Inverse of $x^2-9=y$ is $y=\pm \sqrt{x+9}$ .

Explanation of Solution

Given:

  $x^2-9=y$ .

Concept used:

Inverse of the function is when in addition or subtraction if the two terms made solution $0$ then the two terms are inverse two each other.

In-term of multiplication two term when multiply gives the unity as product then the two terms are inverse two each other.

Calculation:

The function is:

  $x^2-9=y\mathrm{.......}\left(i\right)$

Now, it has to write an equation for the inverse function in the form $y=f^{-1}\left(x\right)$ of the function $\left(i\right)$ it has:

  $\begin{array}{l}{x}^2-9=y.\\ y^2-9=x.\\ y=\pm \sqrt{x+9}.\end{array}$

Hence, the inverse of $x^2-9=y$ is $y=\pm \sqrt{x+9}$ .