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: 59

Answer

$\frac{97}{4}$

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 $(f∘h)(\frac{1}{2})$. We know that $(f∘h)(x)=f(h(x))$. Therefore, $(f∘h)(\frac{1}{2})=f(h(\frac{1}{2}))=f(\frac{1}{2}-5)=f(\frac{1}{2}-\frac{10}{2})= f(\frac{1-10}{2})=f(-\frac{9}{2})=(-\frac{9}{2})^{2}+4=\frac{-9\times-9}{2\times2}+4=\frac{81}{4}+\frac{16}{4}=\frac{81+16}{4}=\frac{97}{4}$.
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