y = f(g(x)) is a composite function in that g(x) is the input to f(x).
y=4/x^2+9 is an example of such a composite function. There's more than one way in which y=4/x^2+9 could be decomposed. For example, if we define f(x) as 4x and g(x) as x^2+9, then f(g(x)) = 4 / [ x^2 + 9], which is the same as the given function. We have replaced "x" in f(x) with g(x), which, in turn, is x^2+9.
Your question, "Finding y=f(g(x)) y=4/x^2+9" could be made more informative. For example, you might phrase this question as "decompose y=4/x^2+9 into functions f(x) and g(x), given that f(g(x)) = y=4/x^2+9."