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

$\left(-\infty, \dfrac{8}{5} \right]$
$\bf{\text{Solution Outline:}}$ The domain of the given function, $f(x)=\sqrt{8-5x} ,$ is all values of $x$ for which the radicand is non-negative. Express the answer in interval notation. $\bf{\text{Solution Details:}}$ Since the radicand of a radical with an even index has to be non-negative, then \begin{array}{l}\require{cancel} 8-5x\ge0 \\\\ -5x\ge-8 .\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} -5x\ge-8 \\\\ x\ge\dfrac{-8}{-5} \\\\ x\le\dfrac{8}{5} .\end{array} Hence the domain is $\left(-\infty, \dfrac{8}{5} \right] .$