Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 2 - 2.6 - Combinations of Functions: Composite Functions - 2.6 Exercises - Page 219: 5


a) $2x$ b) $4$ c) $x^2-4$ d) $\dfrac{x+2}{x-2}$ Domain: $(-\infty,2)\cup(2,\infty)$

Work Step by Step

We are given the functions: $f(x)=x+2$ $g(x)=x-2$ a) Determine $(f+g)(x)$: $(f+g)(x)=f(x)+g)(x)=x+2+x-2=2x$ b) Determine $(f-g)(x)$: $(f-g)(x)=f(x)-g)(x)=x+2-(x-2)=x+2-x+2=4$ c) Determine $(fg)(x)$: $(fg)(x)=f(x)g)(x)=(x+2)(x-2)=x^2-4$ d) Determine $\left(\dfrac{f}{g}\right)(x)$: $\left(\dfrac{f}{g}\right)(x)=\dfrac{x+2}{x-2}$ The domain of $\dfrac{f}{g}$ is the set of all real numbers except the zeros of $g$: $x-2=0\Rightarrow x=2$ The domain is: $(-\infty,2)\cup(2,\infty)$
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