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: 78

Answer

$\color{blue}{[3, 6) \cup (6, 8) \cup (8, 9]}$

Work Step by Step

The graph shows that $F(x)$ covers the x-values from $x=0$ to $x=9$. Thus, its domain is $[1, 9]$. The graph shows that $G(x)$ covers the x-values from $x=3$ to $x=10$. Thus, its domain is $[3, 10]$. The domains of $(F-G)(x)$ and $F \cdot G$ is the intersection (set of common elements) of the domain of $F$ and the domain of $G$. Thus, the domain of $F-G$ and $F \cdot G$ is: $$[1, 9] \cap [3, 10] = [3, 9]$$ The domain of $G/F$ is the intersection of the domain of $F$ and the domain of $G$ excluding the values of $x$ for which $F(x)=0$ Note that $F(6)=0$ and $F(8)=0$. Thus, the domain of $G/F$ does not include $6$ and $8$. Therefore, the domain of $G/F$ is: $$[1, 9] \cap [3, 10] - \left\{6, 8\right\} = [3, 9]-\left\{6, 8\right\}=\color{blue}{[3, 6) \cup (6, 8) \cup (8, 9]}$$
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