Calculus: Early Transcendentals 9th Edition

Published by Cengage Learning
ISBN 10: 1337613924
ISBN 13: 978-1-33761-392-7

Chapter 1 - Section 1.5 - Inverse Functions and Logarithms - 1.5 Exercises - Page 66: 74

Answer

The graph of $y=\tan{x}$, $\frac{\pi}{2} \le x \le \frac{\pi}{2}$ is a reflection about the line $y=x$ of the graph of $y=\tan^{-1}{x}$. Refer to the graph below.

Work Step by Step

Use a graphing calculator to graph the given functions to obtain the graph below. Notice that the graph of $y=\tan{x}$, $-\frac{\pi}{2} \le x \le \frac{\pi}{2}$ is a reflection about the line $y=x$ of the graph of the function $y=\tan^{-1}{x}$.
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