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