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
$u(t)=f\circ g(t)$
