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

$(-\infty,11]$
$\bf{\text{Solution Outline:}}$ The domain of the given function, $f(x)=\sqrt{11-x} ,$ 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} 11-x\ge0 \\\\ -x\ge-11 .\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} -x\ge-11 \\\\ \dfrac{-x}{-1}\ge\dfrac{-11}{-1} \\\\ x\le11 .\end{array} Hence the domain is $(-\infty,11] .$