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: 6


a) $x-3$ b) $3x-7$ c) $-2x^2+9x-10$ d) $\dfrac{2x-5}{2-x}$ Domain: $(-\infty,2)\cup(2,\infty)$

Work Step by Step

We are given the functions: $f(x)=2x-5$ $g(x)=2-x$ a) Determine $(f+g)(x)$: $(f+g)(x)=f(x)+g)(x)=2x-5+2-x=x-3$ b) Determine $(f-g)(x)$: $(f-g)(x)=f(x)-g)(x)=2x-5-(2-x)=2x-5-2+x=3x-7$ c) Determine $(fg)(x)$: $(fg)(x)=f(x)g)(x)=(2x-5)(2-x)=4x-2x^2-10+5x=-2x^2+9x-10$ d) Determine $\left(\dfrac{f}{g}\right)(x)$: $\left(\dfrac{f}{g}\right)(x)=\dfrac{2x-5}{2-x}$ The domain of $\dfrac{f}{g}$ is the set of all real numbers except the zeros of $g$: $2-x=0\Rightarrow x=2$ The domain is: $(-\infty,2)\cup(2,\infty)$
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