Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 7 - Analytic Trigonometry - 7.2 The Inverse Trigonometric Functions (Continued) - 7.2 Assess Your Understanding - Page 457: 1

Answer

domain: $x\in\mathbb{R} \text{ except } x=\frac{(2k+1)\pi}{2}$ (odd integer multiples of $\frac{\pi}{2}$) range: $(-\infty,-1]\cup[1,\infty)$

Work Step by Step

By definition the domain is any real number except $x=\frac{(2k+1)\pi}{2}$, where $k$ is an integer (because $\sec x=\frac{1}{\cos x}$ and $\cos x$ is undefined there), whilst the range is $(-\infty,-1]\cup[1,\infty).$
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