Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Appendix A - Review - A.1 Algebra Essentials - A.1 Assess Your Understanding - Page A11: 75


$\{x\in \mathbb{R}\ |\ x\neq 5\}$

Work Step by Step

The domain of a rational expression is the whole set of real numbers, excluding the numbers that yield zero in the denominator. Here, we exclude $x$ for which the denominator is equal to zero. To find the number/s to be excluded, set the denominator equal to zero, then solve the equation: $x-5=0$ $x=5$ Thus, $5$ has to be excluded from the domain. Hence, the domain of the given expression is $\{x\in \mathbb{R}\ |\ x\neq 5\}$.
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