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: 36


(a) $ 4x^4+12x^2+10$, domain $(-\infty,\infty)$. (b) $ 2x^4+4x^2+5$, domain $(-\infty,\infty)$. (c) $ x^4+2x^2+2$, domain $(-\infty,\infty)$. (d) $ 8x^4+24x^2+21$, domain $(-\infty,\infty)$.

Work Step by Step

Given $f(x)=x^2+1$ and $g(x)=2x^2+3$, we have: (a) $f\circ g=(2x^2+3)^2+1=4x^4+12x^2+10$, domain $(-\infty,\infty)$. (b) $g\circ f=2(x^2+1)^2+3=2x^4+4x^2+5$, domain $(-\infty,\infty)$. (c) $f\circ f=(x^2+1)^2+1=x^4+2x^2+2$, domain $(-\infty,\infty)$. (d) $g\circ g=2(2x^2+3)^2+3=8x^4+24x^2+21$, domain $(-\infty,\infty)$.
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