Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 4 - Section 4.3 - Polynomial Functions, Graphs, and Composition - 4.3 Exercises: 21


a. $-x^{2}+12x-12$, b. $9x^{2}+4x+6$

Work Step by Step

We are given that $f(x)=4x^{2}+8x-3$ and $g(x)=-5x^{2}+4x-9$. We know that $(f+g)(x)=f(x)+g(x)$ and $(f-g)(x)=f(x)-g(x)$. Therefore: $(f+g)(x)=(4x^{2}+8x-3)+(-5x^{2}+4x-9)=4x^{2}-5x^{2}+8x+4x-3-9=-x^{2}+12x-12$. $(f-g)(x)= (4x^{2}+8x-3)-(-5x^{2}+4x-9)=4x^{2}+5x^{2}+8x-4x-3+9=9x^{2}+4x+6$
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