## Calculus 8th Edition

Published by Cengage

# Chapter 1 - Functions and Limits - 1.3 New Functions from Old Functions - 1.3 Exercises - Page 44: 51

#### Answer

$S(t)$ = $(f\circ g\circ h)(t)$ for $h(t)=\cos t,$ $g(t)=\sin t$, and $f(t)=t^{2}$

#### Work Step by Step

$(f\circ g\circ h) (t)=f[g(h(t))]$ If we used a calculator, step by step, for each step, define the operation we would perform on the current result. Starting with $t$, we would 1. calculate the cosine of t ,$\ \ h(t)=\cos t$ 2. calculate the sine of current result, $\ \ g(x)=\sin t$ 3. square the current result , $\ \ f(t)=t^{2}$ $S(t)$ = $(f\circ g\circ h)(t)$ for $h(t)=\cos t,$ $g(t)=\sin t$, and $f(t)=t^{2}$

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