Chapter 7.2, Problem 20PPS

To determine

The inverse of the function $g\left(x\right)=x+4$ and graph the function and its inverse.

Answer to Problem 20PPS

The inverse of function $g\left(x\right)=x+4$ is $g^{-1}\left(x\right)=x-4$ .

Explanation of Solution

Given information: The given function is,

  $g\left(x\right)=x+4$

Concept used: In order to find the inverse of a given function $f\left(x\right)$ write $f\left(x\right)=y$ and exchange the variables $\left(x\right)\text{ and }\left(y\right)$ and solve for the variable $\left(y\right)$ . At last write $y=f^{-1}\left(x\right)$ which is the required inverse of the function $f\left(x\right)$ .

Calculation: For the given function $g\left(x\right)=x+4$ , the inverse is evaluated as,

  $\begin{array}{c}y=x+\mathrm{4......}\left(\text{Plugging }g\left(x\right)=y\right)\\ \text{or, }x=y+\mathrm{4......}\left(\text{Exchanging variables}\right)\\ y=x-\mathrm{4......}\left(\text{Solving for variable }\left(y\right)\right)\\ g^{-1}\left(x\right)=x-\mathrm{4......}\left(\text{Plugging }y=g^{-1}\left(x\right)\right)\end{array}$

Hence, the inverse of function $g\left(x\right)=x+4$ is $g^{-1}\left(x\right)=x-4$ .

Graph: The graph for the function $g\left(x\right)=x+4$ and its inverse function $g^{-1}\left(x\right)=x-4$ is shown as,