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

Chapter 3 - Polynomial and Rational Functions - Section 3.4 Properties of Rational Functions - 3.4 Assess Your Understanding - Page 240: 23

Answer

The domain of $R(x)$ is the set of all real numbers except $3$ and $-3$. In set notation: $\text{Domain:} \{x|x \neq 3, \hspace{5pt} x \neq -3\}$

Work Step by Step

Rational functions are of the form $$R(x)=\dfrac{p(x)}{q(x)}$$ The domain of the rational function is the set of all real numbers except those for which the denominator $q(x)$ is $0$. $\text{Set the denominator equal to zero then solve:}$ $$4(x^2-9)=0\\[3mm] \text{By Factoring:} \\ 4(x-3)(x+3)=0\\ \text{Using the zero product property:}\\ x-3=0 \hspace{10pt} \text{ or }\hspace{10pt} x+3=0\\ x=3 \hspace{10pt} \text{ or }\hspace{10pt} x=-3$$ Thus, the domain of $R(x)$ is the set of all real numbers except $3$ and $-3$. $\text{Domain:} \{x|x \neq 3, \hspace{5pt} x \neq -3\}$
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