Answer
$-\frac{\pi}{2}\lt x\lt\frac{\pi}{2}.$
Work Step by Step
$\tan^{-1}(\tan(x))=x$ where $-\frac{\pi}{2}\lt x\lt\frac{\pi}{2}.$ (as this is the range of $f(x)=\tan^{-1}(x).$)
Precalculus (10th Edition)
by Sullivan, Michael
Published by
Pearson
ISBN 10:
0-32197-907-9
ISBN 13:
978-0-32197-907-0
Chapter 7 - Analytic Trigonometry - 7.1 The Inverse Sine, Cosine, and Tangent Functions - 7.1 Assess Your Understanding - Page 450: 9
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