Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.3 Exercises: 35

Answer

$f(x)$ has an inverse function on the given interval.

Work Step by Step

We find the derivative of $f(x)$: \[ f'(x) = \sec(x)\tan(x) \] On the domain $[0, \frac{\pi}{2})$, both $\sec(x)$ and $\tan(x)$ are nonnegative so $f'(x)$ is nonnegative. Therefore $f(x)$ is strictly monotonic.
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