Answer
a. $ 3-x$
b. $(-\infty,2]$
Work Step by Step
Given $f(x)=x^2+1$ and $g(x)=\sqrt {2-x}, x\leq2$, we have:
a. $(f\circ g)(x)=(\sqrt {2-x})^2+1=3-x$
b. The domain of the above function can be found as $\{x|x\leq2\}$ or $(-\infty,2]$
Precalculus (6th Edition) Blitzer
by Blitzer, Robert F.
Published by
Pearson
ISBN 10:
0-13446-914-3
ISBN 13:
978-0-13446-914-0
Chapter 1 - Section 1.7 - Combinations of Functions; Composite Functions - Exercise Set - Page 259: 74
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