Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 10 - Exponents and Radicals - Mid-Chapter Review - Mixed Review: 8

Answer

$\left( -\infty,10 \right]$

Work Step by Step

$\bf{\text{Solution Outline:}}$ The domain of the given function, $ g(x)=\sqrt[4]{10-x} ,$ is the permissible values of $x.$ $\bf{\text{Solution Details:}}$ With an even index (index equals $ 4 $), then the radicand should be a nonnegative number. Hence, \begin{array}{l}\require{cancel} 10-x\ge0 \\\\ -x\ge-10 \\\\ x\le\dfrac{-10}{-1} \\\\ x\le10 .\end{array} Hence, the domain is the interval $ \left( -\infty,10 \right] .$
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