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 259: 48


$\text{a) } g(x)-f(x)=18x-1 \\\\\text{b) } f(x)g(x)=-77x^2+19x+6 \\\\\text{c) } g(f(x))=-77x+35$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Substitute the given functions, \begin{array}{l}\require{cancel} f(x)= -7x+3 \\g(x)= 11x+2 ,\end{array} into the required operations. $\bf{\text{Solution Details:}}$ a) \begin{array}{l}\require{cancel} g(x)-f(x)=(11x+2)-(-7x+3) \\\\ g(x)-f(x)=11x+2+7x-3 \\\\ g(x)-f(x)=18x-1 \end{array} b) \begin{array}{l}\require{cancel} f(x)g(x)=(-7x+3)(11x+2) \\\\ f(x)g(x)=-7x(11x)-7x(2)+3(11x)+3(2) \\\\ f(x)g(x)=-77x^2-14x+33x+6 \\\\ f(x)g(x)=-77x^2+19x+6 \end{array} c) \begin{array}{l}\require{cancel} g(f(x))=g(-7x+3) \\\\ g(f(x))=11(-7x+3)+2 \\\\ g(f(x))=-77x+33+2 \\\\ g(f(x))=-77x+35 \end{array} Therefore, \begin{array}{l}\require{cancel} \text{a) } g(x)-f(x)=18x-1 \\\\\text{b) } f(x)g(x)=-77x^2+19x+6 \\\\\text{c) } g(f(x))=-77x+35 .\end{array}
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