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 258: 16


$\text{a) } f(g(x))=12x+13 \\\text{b) } g(f(x))=12x-25$

Work Step by Step

$\bf{\text{Solution Outline:}}$ With \begin{array}{l}\require{cancel} f(x)= 3x-8 \\g(x)= 4x+7 ,\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(4x+7) \\\\ f(g(x))=3(4x+7)-8 \\\\ f(g(x))=12x+21-8 \\\\ f(g(x))=12x+13 .\end{array} Replacing $x$ with $f(x)$ in $g$, then \begin{array}{l}\require{cancel} g(f(x))=g(3x-8) \\\\ g(f(x))=4(3x-8)+7 \\\\ g(f(x))=12x-32+7 \\\\ g(f(x))=12x-25 .\end{array} Hence, \begin{array}{l}\require{cancel} \text{a) } f(g(x))=12x+13 \\\text{b) } g(f(x))=12x-25 .\end{array}
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