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: 8

Answer

$a)$ $(f+g)(x)=4x^{3}-6x$ $b)$ $(f-g)(x)=4x^{3}+6x$ $c)$ $(f\cdot g)(x)=-24x^{4}$ $d)$ $\Big(\dfrac{f}{g}\Big)(x)=-\dfrac{2x^{2}}{3}$

Work Step by Step

$f(x)=4x^{3};$ $g(x)=-6x$ For each case, replace $f(x)$ by $4x^{3}$ and $g(x)$ by $-6x$ and simplify if possible: $a)$ $(f+g)(x)$ $f(x)+g(x)=(4x^{3})+(-6x)=4x^{3}-6x$ $b)$ $(f-g)(x)$ $f(x)-g(x)=(4x^{3})-(-6x)=4x^{3}+6x$ $c)$ $(f\cdot g)(x)$ $f(x)\cdot g(x)=(4x^{3})(-6x)=-24x^{4}$ $d)$ $\Big(\dfrac{f}{g}\Big)(x)$ $\dfrac{f(x)}{g(x)}=\dfrac{4x^{3}}{-6x}=-\dfrac{2x^{2}}{3}$
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