College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 2, Functions - Section 2.7 - Combining Functions - 2.7 Exercises - Page 253: 49

Answer

$f \circ g, g \circ f, f \circ f, g \circ g$: for all $D_{f\circ f}=\{x|x \in \mathbb{R} \}$,

Work Step by Step

$f(x)=x^2$, $D_f=\{x|x \in \mathbb{R}\}$ $g(x)=x+1$, $D_g=\{x|x \in \mathbb{R} \}$, $f(g(x))=(x+1)^2=x^2+2x+1$ $D_{f\circ g}=\{x|x \in \mathbb{R} \}$ $g(f(x))=x^2+1$ $D_{g\circ f}=\{x|x \in \mathbb{R} \}$, $f(f(x))=(x^2)^2=x^4$ $D_{f\circ f}=\{x|x \in \mathbb{R} \}$, $g(g(x))=x+1+1=x+2$ $D_{g\circ g}=\{x|x \in \mathbb{R}\}$
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