Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 2 - Section 2.7 - Combining Functions - 2.7 Exercises: 7

Answer

$f+g=3x$ The domain is $(-\infty,\infty)$ $f-g=-x$ The domain is $(-\infty,\infty)$ $fg=2x^{2}$ The domain is $(-\infty,\infty)$ $f/g=\dfrac{1}{2}$ The domain is $(-\infty,\infty)$

Work Step by Step

$f(x)=x$ $;$ $g(x)=2x$ Evaluate the combinations and simplify if possible. Then find the domain of the resulting function: $f+g$ $f(x)+g(x)=x+2x=3x$ This function is defined for all real numbers. The domain is $(-\infty,\infty)$ $f-g$ $f(x)-g(x)=x-2x=-x$ This function is defined for all real numbers. The domain is $(-\infty,\infty)$ $fg$ $f(x)\cdot g(x)=(x)(2x)=2x^{2}$ This function is defined for all real numbers. The domain is $(-\infty,\infty)$ $f/g$ $\dfrac{f(x)}{g(x)}=\dfrac{x}{2x}=\dfrac{1}{2}$ This function is defined for all real numbers. The domain is $(-\infty,\infty)$
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