One approach can be this. We start with given: g(f(x))= something.
Now, we easily conclude: Dom(g(f(x))=Dom(f(x))
Range(g(f(x))=Range(g(y)) (assuming that g is defined over y)
Keeping this in mind we can arbitrarily make two functions out of the given g(f(x)) function so that all the variables are grouped in one function which we will call f(x) and the whole will be g(f(x)).
For example: Given: g(f(x))=3x^2-2x-9. (^ stands for power)
We can arbitrarily say, f(x)=3x^2-2x. So g(y)=y-9#
Now, if we are given some conditions regarding the functions f or g then we can't break g(f(x)) arbitratily. We have to break it in a way that the conditions for f and g are also satisfied.
I hope this helps you. If there are questions then I am interested too.
Smyler wyth nyfe undur the cloke