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

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 9 - Inequalities and Problem Solving - 9.2 Intersections, Unions, and Compound Inequalities - 9.2 Exercise Set - Page 591: 80


$(-\infty,5) \cup (5,\infty)$

Work Step by Step

$\bf{\text{Solution Outline:}}$ The domain of the given function, $ f(x)=\dfrac{2}{x-5} ,$ 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} x-5\ne0 \\\\ x\ne5 .\end{array} Hence the domain is $ (-\infty,5) \cup (5,\infty) .$
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