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: 2

Answer

$a)$ $(f+g)(x)=6x+2$ $b)$ $(f-g)(x)=-4x+6$ $c)$ $(f\cdot g)(x)=5x^{2}+18x-8$ $d)$ $\Big(\dfrac{f}{g}\Big)(x)=\dfrac{x+4}{5x-2}$, where $x\ne\dfrac{2}{5}$

Work Step by Step

$f(x)=x+4;$ $g(x)=5x-2$ For each case, replace $f(x)$ by $x+4$ and $g(x)$ by $5x-2$ and simplify: $a)$ $(f+g)(x)$ $f(x)+g(x)=(x+4)+(5x-2)=x+4+5x-2=6x+2$ $b)$ $(f-g)(x)$ $f(x)-g(x)=(x+4)-(5x-2)=x+4-5x+2=-4x+6$ $c)$ $(f\cdot g)(x)$ $f(x)\cdot g(x)=(x+4)(5x-2)=5x^{2}-2x+20x-8=...$ $...=5x^{2}+18x-8$ $d)$ $\Big(\dfrac{f}{g}\Big)(x)$ $\dfrac{f(x)}{g(x)}=\dfrac{x+4}{5x-2}$ where $x\ne\dfrac{2}{5}$
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