Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 9 - Review: 5



Work Step by Step

We are given that $f(x)=x^{2}-2$, $g(x)=x+1$, and $h(x)=x^{3}-x^{2}$. We know that $(f\circ g)(x)=f(g(x))$. Therefore, $(f\circ g)(x)=f(g(x))=f(x+1)=(x+1)^{2}-2$. We know that a binomial of the form $(a+b)^{2}$ will simplify to $a^{2}+2ab+b^{2}$. Therefore, $(x+1)^{2}-2=x^{2}+2x+1-2=x^{2}+2x-1$.
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