Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 3 - Exponents, Polynomials and Functions - 3.3 Composing Functions - 3.3 Exercises - Page 256: 4


$\text{a) } f(g(x))=-323x+674 \\\text{b) } g(f(x))=-323x+510$

Work Step by Step

$\bf{\text{Solution Outline:}}$ With \begin{array}{l}\require{cancel} f(x)= 19x+28 \\g(x)= -17x+34 ,\end{array} to find $ f(g(x)) ,$ replace $x$ with $g(x)$ in $f.$ To find $g(f(x)),$ replace $x$ with $f(x)$ in $g.$ $\bf{\text{Solution Details:}}$ Replacing $x$ with $g(x)$ in $f$, then \begin{array}{l}\require{cancel} f(g(x))=f(-17x+34) \\\\ f(g(x))=19(-17x+34)+28 \\\\ f(g(x))=-323x+646+28 \\\\ f(g(x))=-323x+674 .\end{array} Replacing $x$ with $f(x)$ in $g$, then \begin{array}{l}\require{cancel} g(f(x))=g(19x+28) \\\\ g(f(x))=-17(19x+28)+34 \\\\ g(f(x))=-323x+476+34 \\\\ g(f(x))=-323x+510 .\end{array} Hence, \begin{array}{l}\require{cancel} \text{a) } f(g(x))=-323x+674 \\\text{b) } g(f(x))=-323x+510 .\end{array}
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