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 - Page 343: 33


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

Work Step by Step

We find the derivative of $f(x)$: \[ f'(x) = -\sin(x) \] On the domain $[0 , \pi]$, $\sin(x)$ is always nonnegative so $f'(x)$ is always nonpositive on the same domain, and $f(x)$ is strictly monotonic.
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