Chapter 8, Problem 10QC

To determine

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

Answer to Problem 10QC

The inverse of the function is $g^{-1}\left(x\right)=2x+1$ and graph for the function and its inverse is shown in figure 1.

Explanation of Solution

Given:

The function is given as $f\left(x\right)=\frac{x-1}{2}$

Calculation:

Replace 1 $f\left(x\right)$ with y in the given equation.

3 $y=\frac{x-1}{2}$

Exchange x and y in the above equation.

  $\begin{array}{l}x=\frac{y-1}{2}\\ 2x=y-1\\ y=2x+1\end{array}$

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

  $g^{-1}\left(x\right)=2x+1$

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

  

Figure 1

Thus, the inverse of the function is $g^{-1}\left(x\right)=2x+1$ and graph for the function and its inverse is shown in figure 1.