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

$\left( -\infty, 7 \right)\cup(7,\infty)$
$\bf{\text{Solution Outline:}}$ The domain of the given function, $f(x)=\dfrac{x}{x-7} ,$ is all the values of $x$ for which the denominator is not equal to $0.$ Express the answer in the interval notation. $\bf{\text{Solution Details:}}$ Since the denominator cannot be zero, then \begin{array}{l}\require{cancel} x-7\ne0 \\\\ x\ne7 .\end{array} Hence, the domain is $\left( -\infty, 7 \right)\cup(7,\infty) .$