Chapter 1 - Functions and Limits - 1.3 New Functions from Old Functions - 1.3 Exercises - Page 44: 47

$v(t)=f\circ g(t)$ for $g(t)=t^{2}$ and $f(t)=\sec t\tan t$

$f\circ g(t)=f[g(t)]$ Rule of thumb: Ask yourself what would be the last operation if we used a calculator, step by step? (Answer: If R$=t^{2}$ was the current result, we would calculate $\sec t\tan t$) $f(t)=\sec t\tan t$ $v(t)=f(t^{2})$ So, if $g(t)=t^{2}$ and $f(t)=\sec t\tan t$, then $v(t)=f\circ g(t)$