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 - Exercise Set: 45

Answer

Given $f(x)$ and $g(x)$ 1. $(f o g)(x) = f(g(x))$ To find this, substitute the entire value of $g(x)$ for $x$ in $f(x)$. For instance, if $f(x) = x^2$ and $g(x) = 3x$, $(f o g)(x) = f(g(x)) = f(3x) = (3x)^2 = 9x^2$ 2. $(g o f)(x) = g(f(x))$ To find this, substitute the entire value of $f(x)$ for $x$ in $g(x)$. For instance, if $f(x) = x^2$ and $g(x) = 3x$, $(g o f)(x) = g(f(x)) = g(x^2) = 3(x^2) = 3x^2$

Work Step by Step

Given $f(x)$ and $g(x)$ 1. $(f o g)(x) = f(g(x))$ To find this, substitute the entire value of $g(x)$ for $x$ in $f(x)$. For instance, if $f(x) = x^2$ and $g(x) = 3x$, $(f o g)(x) = f(g(x)) = f(3x) = (3x)^2 = 9x^2$ 2. $(g o f)(x) = g(f(x))$ To find this, substitute the entire value of $f(x)$ for $x$ in $g(x)$. For instance, if $f(x) = x^2$ and $g(x) = 3x$, $(g o f)(x) = g(f(x)) = g(x^2) = 3(x^2) = 3x^2$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.