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: 21


$\text{a) } f(g(x))=2.4276x+6.7732 \\\\\text{b) } g(f(x))=2.4276x+14.9152$

Work Step by Step

$\bf{\text{Solution Outline:}}$ With \begin{array}{l}\require{cancel} f(x)= 0.68x+2.36 \\g(x)= 3.57x+6.49 ,\end{array} replace $x$ with $g(x)$ in $f$ to find $f(g(x)).$ 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( 3.57x+6.49 ) \\\\ f(g(x))=0.68(3.57x+6.49)+2.36 \\\\ f(g(x))=2.4276x+4.4132+2.36 \\\\ f(g(x))=2.4276x+6.7732 .\end{array} Replacing $x$ with $f(x)$ in $g.$ Hence, \begin{array}{l}\require{cancel} g(f(x))=g(0.68x+2.36) \\\\ g(f(x))=3.57(0.68x+2.36)+6.49 \\\\ g(f(x))=2.4276x+8.4252+6.49 \\\\ g(f(x))=2.4276x+14.9152 .\end{array} Hence, \begin{array}{l}\require{cancel} \text{a) } f(g(x))=2.4276x+6.7732 \\\\\text{b) } g(f(x))=2.4276x+14.9152 .\end{array}
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