Answer
$x^{2}-1$
Work Step by Step
We are given that $f(x)=x^{2}+4$, $g(x)=2x+3$, and $h(x)=x-5$.
We are asked to find $(h∘f)(x)$. We know that $(h∘f)(x)=h(f(x))$.
Therefore, $(h∘f)(x)=h(x^{2}+4)=(x^{2}+4)-5=x^{2}+4-5=x^{2}-1$.
Intermediate Algebra (12th Edition)
by Lial, Margaret L.; Hornsby, John; McGinnis, Terry
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 - Page 296: 58
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