Chapter 8, Problem 14QC

To determine

To find: The value of $f^{-1}\left(x\right)$ and explain.

Answer to Problem 14QC

The value of $f^{-1}\left(x\right)$ is $\frac{1}{2}\left(x-12\right)$ .

Explanation of Solution

Given:

The equation represents $f\left(x\right)=2x+12$

Calculation:

For the given equation, a pizzeria charges $12 for pizza and additional $2 for each topping. Here x denotes the number of topping for a pizza.

Replace $f\left(x\right)$ with y in the given equation.

  $y=2x+12$

Exchange x and y in the above equation.

  $\begin{array}{l}x=2y+12\\ x-12=2y\\ y=\frac{1}{2}\left(x-12\right)\end{array}$

Replace y with $f^{-1}\left(x\right)$ .

  $f^{-1}\left(x\right)=\frac{1}{2}\left(x-12\right)$

Thus, the value of $f^{-1}\left(x\right)$ is $\frac{1}{2}\left(x-12\right)$ .