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: 74


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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 denominator = 0 $ x^{3}+x=0\qquad$... factor out x... $x(x^{2}+1)=0$ By the zero product principle, at least one of the factors is zero. $x^{2}+1$ is never zero, because $x^{2}\geq 0$. So, the only number to exclude from the domain is $x=0$.
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