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

$(-\infty,4) \cup (4,\infty)$
$\bf{\text{Solution Outline:}}$ The domain of the given function, $f(x)=\dfrac{x+3}{2x-8} ,$ is all values of $x$ for which the denominator is not $0.$ Express the answer in interval notation. $\bf{\text{Solution Details:}}$ Since the denominator of the given function cannot be $0$, then \begin{array}{l}\require{cancel} 2x-8\ne0 \\\\ 2x\ne8 \\\\ x\ne\dfrac{8}{2} \\\\ x\ne4 .\end{array} Hence the domain is $(-\infty,4) \cup (4,\infty) .$