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: 50


$H(x)$ = $(f\circ g\circ h)(x)$ for $h(x)=|x|,$ $g(x)=2+x$, and $f(x)=\sqrt[8]{x}$

Work Step by Step

$(f\circ g\circ h) (x)=f[g(h(x))]$ If we used a calculator, step by step, for each step, define the operation we would perform on the current result. Starting with x, we would 1. calculate $|x|,\ \ \ h(x)=|x|$ 2. add 2 to the current result, $\ \ g(x)=x+2$ 3. if the current result was R, calculate $\sqrt[8]{R},\ \ \ f(x)=\sqrt[8]{x}$ $H(x)$ = $(f\circ g\circ h)(x)$ for $h(x)=|x|,$ $g(x)=2+x$, and $f(x)=\sqrt[8]{x}$
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