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: 34

Answer

(a) $ x^2+5$, domain $(-\infty,\infty)$. (b) $ x^2+2x+5$, domain $(-\infty,\infty)$. (c) $ x+2$, domain $(-\infty,\infty)$. (d) $ x^4+8x^2+20$, domain $(-\infty,\infty)$.

Work Step by Step

Given $f(x)=x+1$ and $g(x)=x^2+4$, we have: (a) $f\circ g=(x^2+4)+1=x^2+5$, domain $(-\infty,\infty)$. (b) $g\circ f=(x+1)^2+4=x^2+2x+5$, domain $(-\infty,\infty)$. (c) $f\circ f=(x+1)+1=x+2$, domain $(-\infty,\infty)$. (d) $g\circ g=(x^2+4)^2+4=x^4+8x^2+20$, domain $(-\infty,\infty)$.
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