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: 60

Answer

$-\frac{3}{4}$

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 $(h∘f)(\frac{1}{2})$. We know that $(h∘f)(x)=h(f(x))$. Therefore, $(h∘f)(\frac{1}{2})=h(f(\frac{1}{2})=h((\frac{1}{2})^{2}+4)=h(\frac{1}{4}+4)=(\frac{1}{4}+ \frac{16}{4})=h(\frac{1+16}{4})=h(\frac{17}{4})=\frac{17}{4}-5=\frac{17}{4}-\frac{20}{4}=\frac{17-20}{4}=\frac{-3}{4}=-\frac{3}{4}$.
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