Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 4 - Exponential and Logarithmic Functions - Section 4.1 Composite Functions - 4.1 Assess Your Understanding - Page 280: 33


(a) $ 3x^2+1$, domain $(-\infty,\infty)$. (b) $ 9x^2+6x+1$, domain $(-\infty,\infty)$. (c) $ 9x+4$, domain $(-\infty,\infty)$. (d) $ x^4$, domain $(-\infty,\infty)$.

Work Step by Step

Given $f(x)=3x+1$ and $g(x)=x^2$, we have: (a) $f\circ g=3(x^2)+1=3x^2+1$, domain $(-\infty,\infty)$. (b) $g\circ f=(3x+1)^2=9x^2+6x+1$, domain $(-\infty,\infty)$. (c) $f\circ f=3(3x+1)+1=9x+4$, domain $(-\infty,\infty)$. (d) $g\circ g=(x^2)^2=x^4$, domain $(-\infty,\infty)$.
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.