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: 9

Answer

$f+g=2x^{2}+x$ The domain is $(-\infty,\infty)$ $f-g=x$ The domain is $(-\infty,\infty)$ $fg=x^{4}+x^{3}$ The domain is $(-\infty,\infty)$ $f/g=\dfrac{x^{2}+x}{x^{2}}$ The domain is $(-\infty,0)\cup(0,\infty)$ or $\{x|x\ne0\}$

Work Step by Step

$f(x)=x^{2}+x$ $;$ $g(x)=x^{2}$ Evaluate the combinations and simplify if possible. Then , find the domains of the resulting functions: $f+g$ $f(x)+g(x)=(x^{2}+x)+(x^{2})=2x^{2}+x$ This function is defined for all real numbers. The domain is $(-\infty,\infty)$ $f-g$ $f(x)-g(x)=(x^{2}+x)-(x^{2})=x$ This function is defined for all real numbers. The domain is $(-\infty,\infty)$ $fg$ $f(x)\cdot g(x)=(x^{2}+x)(x^{2})=x^{4}+x^{3}$ This function is defined for all real numbers. The domain is $(-\infty,\infty)$ $f/g$ $\dfrac{f(x)}{g(x)}=\dfrac{x^{2}+x}{x^{2}}$ This function is undefined for all the values of $x$ that make the denominator equal to $0$. To find these values, set the denominator equal to $0$ and solve the equation: $x^{2}=0$ $x=0$ The domain is $(-\infty,0)\cup(0,\infty)$ or $\{x|x\ne0\}$
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