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: 7

Answer

$a)$ $(f+g)(x)=5x^{2}-3x$ $b)$ $(f-g)(x)=-5x^{2}-3x$ $c)$ $(f\cdot g)(x)=-15x^{3}$ $d)$ $\Big(\dfrac{f}{g}\Big)(x)=-\dfrac{3}{5x}$, where $x\ne0$

Work Step by Step

$f(x)=-3x;$ $g(x)=5x^{2}$ For each case, replace $f(x)$ by $-3x$ and $g(x)$ by $5x^{2}$ and simplify if possible: $a)$ $(f+g)(x)$ $f(x)+g(x)=(-3x)+(5x^{2})=5x^{2}-3x$ $b)$ $(f-g)(x)$ $f(x)-g(x)=(-3x)-(5x^{2})=-5x^{2}-3x$ $c)$ $(f\cdot g)(x)$ $f(x)\cdot g(x)=(-3x)(5x^{2})=-15x^{3}$ $d)$ $\Big(\dfrac{f}{g}\Big)(x)$ $\dfrac{f(x)}{g(x)}=\dfrac{-3x}{5x^{2}}=\dfrac{-3}{5x}=-\dfrac{3}{5x}$, where $x\ne0$
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