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

, where

Choice #3)

Now try . Note that (actually, it can't be allowed to be 0). Have .

Thus and , so

Thus

(now use to know that )

, where

Choice #4)