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: 31

Answer

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

Work Step by Step

We find the derivative of $f(x)$: \[ f'(x) = -\frac{8}{x^3} \] When the domain is from $(0, \infty)$, $x^3$ is always positive so $f'(x)$ is always negative. Therefore, $f(x)$ is strictly monotonic.
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