College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 2 - Section 2.8 - Function Operations and Composition - 2.8 Exercises - Page 266: 4



Work Step by Step

$\bf{\text{Solution Outline:}}$ To evaluate the given expression, $ (f-g)(4) ,$ given \begin{array}{l}\require{cancel} f(x)=x^2+3 \\ g(x)=-2x+6 ,\end{array} use the definition of the appropriate function operation. Then substitute $x$ with $ 4 .$ $\bf{\text{Solution Details:}}$ Since $(f-g)(x)=f(x)-g(x),$ then \begin{array}{l}\require{cancel} (f-g)(x)=(x^2+3)-(-2x+6) \\\\ (f-g)(x)=x^2+3+2x-6 \\\\ (f-g)(x)=x^2+2x-3 .\end{array} Substituting $x$ with $ 4 ,$ then \begin{array}{l}\require{cancel} (f-g)(4)=(4)^2+2(4)-3 \\\\ (f-g)(4)=16+8-3 \\\\ (f-g)(4)=21 .\end{array}
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