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: 77

Answer

domain of $F(x)$: $[1, 9]$ domain of $G(x)$: $[3, 10]$. domain of $(F+G)(x)$: $[3, 9]$ domain of $F/G$: $[3, 9]$

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 domain of $(F+G)(x)$ is the intersection (set of common elements) of the domain of $F$ and the domain of $G$. Thus, the domain of $F+G$ is: $$[1, 9] \cap [3, 10] = [3, 9]$$ The domain of $F/G$ is the intersection of the domain of $F$ and the domain of $G$ excluding the values of $x$ for which $G(x)=0$ Since there is no $x$ where $G(x) = 0$, then the domain of $F/G$ is: $$[1, 9] \cap [3, 10] = [3, 9]$$
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