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: 28

Answer

$f(x)$ does not have an inverse function.

Work Step by Step

We find the derivative of $f(x)$: \[ f'(x) = - \sin \left ( \frac{3x}{2} \right ) \cdot \frac{3}{2} \] The sine function oscillates between positive and negative outputs so $f(x)$ is not strictly monotonic.
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