Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 7 - Functions and Graphs - 7.4 The Algebra of Functions - 7.4 Exercise Set: 71

Answer

$\color{blue}{(-\infty, -2.5) \cup (-2.5, -1) \cup (-1, +\infty)}$

Work Step by Step

Find the domain of each function: For $f(x)$, the value of $x$ cannot be $-1$ since it will make the denominator zero. . Thus, the domain of $f(x)$ is $(-\infty, -1) \cup (-1, +\infty)$. For $g(x)$, the value of $x$ can be any real number. Thus, the domain of $g(x)$ is $(-\infty, +\infty)$. RECALL: The domain of the $(f/g)(x)$ is the common elements of the domains of $f(x)$ and $g(x)$ excluding $x$ values for which $g(x)=0$. Note that when $g(-2.5)=0$. Thus, the domain of $(f/g)(x)$ is the set of all real numbers except $-1$ and $-2.5$. In interval notation, the domain of $f/g$ is: $\color{blue}{(-\infty, -2.5) \cup (-2.5, -1) \cup (-1, +\infty)}$
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