# Chapter 10 - Exponents and Radicals - Mid-Chapter Review - Mixed Review - Page 663: 8

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

#### 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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