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

$\left(-\infty,\dfrac{5}{7} \right]$
$\bf{\text{Solution Outline:}}$ The domain of the given function, $d(x)=-\sqrt[4]{5-7x} ,$ 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} 5-7x\ge0 \\\\ -7x\ge-5 .\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} -7x\ge-5 \\\\ x\le\dfrac{-5}{-7} \\\\ x\le\dfrac{5}{7} .\end{array} Hence, the domain is the interval $\left(-\infty,\dfrac{5}{7} \right] .$