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: 64

Answer

$\color{blue}{(-\infty, 0.25) \cup (0.25, 3) \cup (3, +\infty)}$

Work Step by Step

Find the domain of each function: For $f(x)$, the value of $x$ can be any real number except 3 since it will make the denominator zero, which is not allowed. Thus, domain of $f(x)$ is $(-\infty, 3) \cup (3, +\infty)$ For $f(x)$, the value of $x$ can be any real number except $0.25$ since it will make the denominator zero, which is not allowed. Thus, domain of $f(x)$ is $(-\infty, 0.25) \cup (0.25, +\infty)$ 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. Note that: $[(-\infty, 3) \cup(3, +\infty)] \cap [(-\infty, 0.25) \cup (0.25, +\infty)] \\= (-\infty, 0.25) \cup (0.25, 3) \cup (3, +\infty)$. Thus, the domain of the sum, difference, and product of $f(x)$ and $g(x)$ is: $\color{blue}{(-\infty, 0.25) \cup (0.25, 3) \cup (3, +\infty)}$
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