Answer
$[0,\pi]$.
Work Step by Step
From the definition of the trig inverse functions, the range for $y=cos^{-1}(x)$ is $y\in[0,\pi]$. Thus for $x=cos^{-1}(cos(x))$, the restriction for $x$ is $x\in[0,\pi]$.
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)
by Sullivan III, Michael
Published by
Pearson
ISBN 10:
0-32193-104-1
ISBN 13:
978-0-32193-104-7
Chapter 6 - Analytic Trigonometry - Section 6.1 The Inverse Sine, Cosine, and Tangent Functions - 6.1 Assess Your Understanding - Page 473: 8
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