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: 32


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

Work Step by Step

We find the derivative of $f(x)$: \[ f'(x) = - \csc ^2 (x) = - \frac{1}{\sin^2(x)} \] Notice that on the domain $(0, \pi)$, $\sin(x)$ is always positive. Therefore, on the same domain, $f'(x)$ is always negative, and $f(x)$ is strictly monotonic.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.