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

$(-\infty,5]$
$\bf{\text{Solution Outline:}}$ The domain of the given function, $g(x)=\sqrt[4]{10-2x} ,$ 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} 10-2x\ge0 \\\\ -2x\ge-10 .\end{array} Dividing both sides by a negative number (and consequently reversing the inequality symbol) the inequality above is equivalent to \begin{array}{l}\require{cancel} -2x\ge-10 \\\\ x\le\dfrac{-10}{-2} \\\\ x\le5 .\end{array} Hence, the domain is the interval $(-\infty,5] .$