Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 1 - Functions and Limits - 1.3 New Functions from Old Functions - 1.3 Exercises - Page 44: 41


$(f\circ g\circ h) (x)=\sqrt{x^{6}+4x^{3}+1}$

Work Step by Step

$(f\circ g\circ h) (x)=f[g(h(x))]$ $g(h(x))=[h(x)]^{2}=(x^{3}+2)^{2}$ $f[g(h(x))]=f[(x^{3}+2)^{2}]=\sqrt{(x^{3}+2)^{2}-3}$ $=\sqrt{(x^{6}+4x^{3}+4)-3}$ $=\sqrt{x^{6}+4x^{3}+1}$
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