Answer
$2sec(\frac{1}{2}x)$,
$sec(x)$.
See graph.
Work Step by Step
Step 1. Given $f(x)=2sec(x)$ and $g(x)=\frac{1}{2}x$, we have $(f\circ g)(x)=f(g(x))=2sec(\frac{1}{2}x)$,
Step 2. We have $(g\circ f)(x)=g(f(x))=\frac{1}{2}2sec(x)=sec(x)$.
Step 3. See graph.