I'm assuming all of (x^2+9) is in the denominator. If that assumption is correct, then,
One possible answer is [tex]f(x) = \frac{4}{x}, \ \ g(x) = x^2+9[/tex]
Another possible answer is [tex]f(x) = \frac{4}{x+9}, \ \ g(x) = x^2[/tex]
There are many ways to do this. The idea is that when we have f( g(x) ), we basically replace every x in f(x) with g(x)
So in the first example above, we would have
[tex]f(x) = \frac{4}{x}\\\\f( g(x) ) = \frac{4}{g(x)}\\\\f( g(x) ) = \frac{4}{x^2+9}[/tex]
In that third step, g(x) was replaced with x^2+9 since g(x) = x^2+9.
Similar steps will happen with the second example as well (when g(x) = x^2)
