Chapter 7, Problem 6QC

To determine

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

Answer to Problem 6QC

The inverse of the function is $g^{-1}\left(x\right)=\frac{x-5}{2}$ and graph for the function and its inverse is shown in figure 1.

Explanation of Solution

Given:

The function is given as $f\left(x\right)=2x+5$

Calculation:

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

  $y=2x+5$

Exchange x and y in the above equation.

  $\begin{array}{l}x=2y+5\\ 2y=x-5\\ y=\frac{x-5}{2}\end{array}$

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

  $g^{-1}\left(x\right)=\frac{x-5}{2}$

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

  

Figure 1

Thus, the inverse of the function is $g^{-1}\left(x\right)=\frac{x-5}{2}$ and graph for the function and its inverse is shown in figure 1.