Chapter 8, Problem 9QC

To determine

To find: The inverse of the function and graph for the function and its inverse.

Answer to Problem 9QC

The inverse of the function is $g^{-1}\left(x\right)=4\left(x+3\right)$ and graph for the function and its inverse is shown in figure 1.

Explanation of Solution

Given:

The function is given as $f\left(x\right)=\frac{1}{4}x-3$

Calculation:

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

  $y=\frac{1}{4}x-3$

Exchange x and y in the above equation.

  $\begin{array}{l}x=\frac{1}{4}y-3\\ x+3=\frac{1}{4}y\\ y=4\left(x+3\right)\end{array}$

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

  $g^{-1}\left(x\right)=4\left(x+3\right)$

The graph for the function and its inverse is shown in figure 1.

  

Figure 1

Thus, the inverse of the function is $g^{-1}\left(x\right)=4\left(x+3\right)$ and graph for the function and its inverse is shown in figure 1.