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: 22


The domain of $G(x)$ is the set of all real numbers.

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 $0$. $\text{Set the denominator equal to zero then solve:}$ $$x^4+1=0\\ x^4=-1\\ \text{ This equation has no real roots because any real number raised} \\\text{ to the fourth power will never be negative.}$$ Thus, the domain of $G(x)$ is the set of all real numbers.
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