Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 4 - Polynomial and Rational Functions - 4.2 Properties of Rational Functions - 4.2 Assess Your Understanding - Page 197: 22


All real numbers except $-1$ and $1$.

Work Step by Step

Factor the denominator to obtain: $x^4-1=(x^2-1)(x^2+1)=(x+1)(x-1)(x^2+1)$ The denominator cannot be $0$. Hence . $(x+1)(x-1)(x^2+1)\ne0\\ \longrightarrow x+1 \ne0, x-1\ne0, \text{ and } x^2+1\ne0\\ \longrightarrow x\ne-1, x\ne1 \space \space(x^2+1\text{ has no restrictions)}$ Therefore the domain of the given function is the set of all real numbers except $-1$ and $1$.
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