Intermediate Algebra (6th Edition)

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

Chapter 9 - Review: 8

Answer

$x^{4}-4x^{2}+2$

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 $(f\circ f)(x)=f(f(x))$. Therefore, $(f\circ f)(x)=f(f(x))=f(x^{2}-2)=(x^{2}-2)^{2}-2$ We know that a binomial of the form $(a-b)^{2}$ will simplify to $a^{2}-2ab+b^{2}$. Therefore, $(x^{2}-2)^{2}-2=(x^{2\times2}-2(2x^{2})+4)-2=x^{4}-4x^{2}+2$.
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