Chapter 8, Problem 8QC

To determine

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

Answer to Problem 8QC

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

Explanation of Solution

Given:

The function is given as $f\left(x\right)=-4x$

Calculation:

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

  $y=-4x$

Exchange x and y in the above equation.

  $\begin{array}{l}x=-4y\\ y=-\frac{1}{4}x\end{array}$

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

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

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

  

Figure 1

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