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: 53

Answer

(a) $f(g(x))=5.25x+18$ (b) $g(f(6))=56.25$ (c) $g(x)-f(x)=2x+4.5$

Work Step by Step

$f(x)=1.5x+4.5$ $g(x)=3.5x+9$ (a) Determine $f(g(x))$: $f(g(x))=f(3.5x+9)$ $=2.5(3.5x+9)+4.5$ $=5.25x+13.5+4.5$ $=5.25x+18$ (b) Determine $g(f(x))$: $g(f(x))=g(1.5x+4.5)$ $= 3.5(1.5x+4.5)+9$ $=5.25x+15.75+9$ $=5.25x+24.75$ $g(f(x))=5.25x+24.75$ Put $x=6$ in $g(f(x))$: $g(f(6))=5.25(6)+24.75=56.25$ (c) Determine $g(x)-f(x)$: $g(x)-f(x)=(3.5x+9)-(1.5x+4.5)$ $=3.5x+9-1.5x-4.5$ $=2x+4.5$
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