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 - Page 296: 62



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 $(g∘f)(-\frac{1}{2})$. We know that $(g∘f)(x)=g(f(x))$. Therefore, $(g∘f)(-\frac{1}{2})=g(f(-\frac{1}{2}))=g((-\frac{1}{2})^{2}+4)=g(\frac{-1\times-1}{2\times2}+4)=g(\frac{1}{4}+\frac{16}{4})=g(\frac{1+16}{4})=g(\frac{17}{4})=2(\frac{17}{4})+3=\frac{2\times17}{4}+\frac{12}{4}=\frac{34}{4}+\frac{12}{4}=\frac{34+12}{4}=\frac{46}{12}=\frac{46\div2}{12\div2}=\frac{23}{6}$.
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