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: 48

Answer

$u(t)=f\circ g(t)$ for $g(x)=\tan t$ and $f(t)=\displaystyle \frac{t}{1+t}$

Work Step by Step

$f\circ g(t)=f[g(t)]$ Rule of thumb: Ask yourself what would be the last operation if you used a calculator, step by step? (Answer: If R=$\tan t$ was the current result, we would calculate $\displaystyle \frac{R}{1+R}$) $f(R)=\displaystyle \frac{R}{1+R}$ $u(t)=f(\tan t)$ So, if $g(t)=\tan t$ and $f(t)=\displaystyle \frac{t}{1+t}$, then $u(t)=f\circ g(t)$
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