Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 12 - Section 12.1 - The Algebra of Functions - Practice: 2

Answer

$\begin{align} \textbf{(a)}&(f\bullet g)(3)=49\\&(g\bullet f)(3)=19 \end{align}$ $\begin{align} \textbf{(b)}&(f\bullet g)(x)=4x^2+4x+1\\&(g\bullet f)(x)=2x^2+1 \end{align}$

Work Step by Step

$f(x)=x^2$ and $g(x)=2x+1$ (a) $(f\bullet g)(3)$ and $(g\bullet f)(3)$ $\begin{align} (f\bullet g)(3)&=f(g(3))\\&=f(2(3)+1)\\&=f(7)\\&=7^2=49 \end{align}$ $\begin{align} (g\bullet f)(3)&=g(f(3))\\&=g(3^2)\\&=g(9)\\&=2(9)+1\\&=18+1=19 \end{align}$ (b) $(f\bullet g)(x)$ and $(g\bullet f)(x)$ $\begin{align} (f\bullet g)(x)&=f(g(x))\\&=f(2x+1)\\&=(2x+1)^2\\&=4x^2+4x+1 \end{align}$ $\begin{align} (g\bullet f)(x)&=g(f(x))\\&=g(x^2)\\&=2x^2+1 \end{align}$
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