Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 1 - Precalculus Review - 1.3 The Basic Classes of Functions - Exercises - Page 23: 29


$(f \circ g)(x) = 2^{x^2}$, $(g \circ f)(x) = 2^{2x}$. Domains: $\mathbb{R}$

Work Step by Step

We have the composite functions: $(f \circ g)(x) = f(g(x)) = f(x^{2}) = 2^{x^2}$, $(g \circ f)(x) = g(f(x)) = g(2^{x}) = (2^{x})^{2} = 2^{2x}$. The domains $D_f, D_g$ are the same and equal to $\mathbb{R}$. Similarly, the domains of the compositions $f \circ g$ and $g \circ f$ are the same and equal to $\mathbb{R}$.
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