Chapter 4.7, Problem 20E

To determine

Sketch the graph and verify that g is inverse of f

Answer to Problem 20E

graph of $g$ is the inverse of $f$ .

Explanation of Solution

Given:

  $\begin{array}{l}f\left(x\right)=tanx\hfill \\ g\left(x\right)=arctanx\hfill \\ y=x\hfill \end{array}$

Use Ti-83 calculator to graph the above-mentioned functions in the same viewing window.

Step 1: Set the coordinates of the viewing window such that $Xmin=–\pi /2andXmax=\pi /2$ be the range as shown below

  

Step 2: Press Y= to enter the following functions

  $\begin{array}{l}{Y}_1=\tan (x)\hfill \\ Y_2={\tan }^{-1}(x)\hfill \\ Y_3=x\hfill \end{array}$

The displays is as shown below

  

Step 3: Press the GRAPH button to get the graph as shown below

  

As in the above figure of step 3, the graph of $Y_2$ is an image of $Y_1$ about the line $Y_3$ .

Hence, graph of $g$ is the inverse of $f$ .