College Algebra 7th Edition

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

Chapter 2, Functions - Chapter 2 Review - Exercises: 87

Answer

$1+\sqrt{x}$

Work Step by Step

We are given: $f(x)=\sqrt{1-x}$, $g(x)=1-x^{2}$ and $h(x)=1+\sqrt{x}$ We evaluate: $(f\circ g\circ h)(x)=f(g(h(x)))=f(g(1+\sqrt{x}))=f(1-(1+\sqrt{x})^{2})=f(1-(1+2\sqrt{x}+x))=f(1-1-2\sqrt{x}-x)=f(-2\sqrt{x}-x)=\sqrt{1-(-2\sqrt{x}-x)}=\sqrt{1+2\sqrt{x}+x}=\sqrt{(1+\sqrt{x})^{2}}=1+\sqrt{x}$
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