Your answer was a quotient, not a composition. You found f and g so that h(x) = f(x)/g(x).
There are an unlimited number of choices given the way the problem is stated.
For instance, there are always these trivial choices:
Choice #1) f(x) = h(x) and g(x) = x
Choice #2) f(x) = x and g(x) = h(x)
Maybe more interesting is letting g(x) = x+5.
Then and , so
Now try . Note that (actually, it can't be allowed to be 0). Have .
Thus and , so
(now use to know that )