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 269: 56

Answer

$(f\circ g)(7)=9$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To evaluate the given expression, $ (f\circ g)(7) ,$ use the definition of function composition. Use the given table for the values of the function. $\bf{\text{Solution Details:}}$ Since $(f\circ g)(x)=f(g(x)),$ then \begin{array}{l}\require{cancel} (f\circ g)(7)=f(g(7)) .\end{array} Based on the table, the value of $ g $ when $x= 7 $ is $ 6 .$ Hence, $ g(7)=6 .$ By substitution, the equation above becomes \begin{array}{l}\require{cancel} (f\circ g)(7)=f(g(7)) \\\\ (f\circ g)(7)=f(6) .\end{array} Based on the table, the value of $ f $ when $x= 6 $ is $ 9 .$ Hence, $ f(6)=9 .$ By substitution, the equation above becomes \begin{array}{l}\require{cancel} (f\circ g)(7)=f(g(7)) \\\\ (f\circ g)(7)=f(6) \\\\ (f\circ g)(7)=9 .\end{array}
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