Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 12 - Section 12.1 - The Algebra of Functions - Exercise Set - Page 842: 6


$a)$ $(f+g)(x)=\sqrt[3]{x}+x-3$ $b)$ $(f-g)(x)=\sqrt[3]{x}-x+3$ $c)$ $(f\cdot g)(x)=x\sqrt[3]{x}-3\sqrt[3]{x}$ $d)$ $\Big(\dfrac{f}{g}\Big)(x)=\dfrac{\sqrt[3]{x}}{x-3}$, where $x\ne3$

Work Step by Step

$f(x)=\sqrt[3]{x};$ $g(x)=x-3$ For each case, replace $f(x)$ by $\sqrt[3]{x}$ and $g(x)$ by $x-3$ and simplify if possible: $a)$ $(f+g)(x)$ $f(x)+g(x)=(\sqrt[3]{x})+(x-3)=\sqrt[3]{x}+x-3$ $b)$ $(f-g)(x)$ $f(x)-g(x)=(\sqrt[3]{x})-(x-3)=\sqrt[3]{x}-x+3$ $c)$ $(f\cdot g)(x)$ $f(x)\cdot g(x)=(\sqrt[3]{x})(x-3)=x\sqrt[3]{x}-3\sqrt[3]{x}$ $d)$ $\Big(\dfrac{f}{g}\Big)(x)$ $\dfrac{f(x)}{g(x)}=\dfrac{\sqrt[3]{x}}{x-3}$, where $x\ne3$
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