Calculus 10th Edition

Published by Brooks Cole

Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.3 Exercises - Page 343: 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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