Chapter 4.7, Problem 31PPS

To determine

To write: the inverse of given function $f^{-1}(x)$ in notation.

Explanation of Solution

Given information:

Consider the function $f(x)=\frac{1}{4}x-1$

Find the inverse of $f(x)=\frac{1}{4}x-1$

Let $y=f(x)=\frac{1}{4}x-1$

  $\begin{array}{l}y=\frac{1}{4}x-1\\ y+1=\frac{1}{4}x\\ x=4y+4\\ f^{-1}(y)=4y+4\\ f^{-1}(x)=4x+4\end{array}$

The graph of $f^{-1}(x)=4x+4$ is shown below

Hence, $f^{-1}(x)=4x+4$