$f(x) =$_____________
$g(x) =\operatorname{cos}x$

One possible solution:
$f(x) = x^³$
$g(x) = 3x\operatorname{cos}(x^²)$
Find another.

One possible solution:
$f(x) = x^0$
$g(x) = x^2$
Find another.

Recall the definition of inverse functions:
$f(x)$ and $g(x)$ are inverse functions if $f(g(x)) = x$