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: 58


$f(x)=\sqrt x$ and $g(x)=1-x^2$

Work Step by Step

We wish to find two functions $f$ and $g$ such that: $H(x)=(f \circ g)(x) =\sqrt {1-x^2}$ Let us consider: $f(x)=\sqrt x$ and $g(x)=1-x^2$ Then we have the composite function: $H(x)=(f \circ g)(x) =f[g(x)]=f(1-x^2)=\sqrt {1-x^2}$
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