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: 57

Answer

$\color{blue}{(-\infty, -5) \cup (-5, +\infty)}$

Work Step by Step

RECALL: The domain of the sum, difference, and product of $f(x)$ and $g(x)$ is the common elements of the domains of the two functions. The domain of the respective functions are: $f(x)$ is defined for all real numbers except $-5$ (since 5 will make the denominator zero) so its domain is: $(-\infty, 5) \cup (5, +\infty)$ $g(x)$ is defined for all real numbers so its domain is: $(-\infty, +\infty)$ Note that: $[(-\infty, -5) \cup(-5, +\infty)] \cap (-\infty, +\infty) \\= (-\infty, -5) \cup (-5, +\infty)$. Thus, the domain of the sum, difference, and product of $f(x)$ and $g(x)$ is: $\color{blue}{(-\infty, -5) \cup (-5, +\infty)}$
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