Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 9 - Section 9.1 - The Algebra of Functions; Composite Functions - Vocabulary, Readiness & Video Check - Page 540: 7

Answer

Let $f(x)=2x+1$ and $g(x)=x-4$ for this problem. $f(x)=2x+1$ $f(2)=2*2+1$ $f(2)=4+1$ $f(2)=5$ $g(x)=x-4$ $g(2)=2-4$ $g(2)=-2$

Work Step by Step

One way to find $(f+g)(x)$ is to add the functions together. $(f+g)(x) = (2x+1) + (x-4) = 2x+1+x-4 = 3x-3$ Another way to find $(f+g)(x)$ is to take the composition of the two functions. $f(g(x)) = f(x-4) = 2(x-4)+1 = 2x-8+1 = 2x-7$.
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