Suppose f(x) and g(x) are non zero polynomials such that f(g(x))=f(x).g(x). If g(2) is 37. Find the value of g(3).
I'm just wondering if you could give us a bit of context for the problem.
What kind of class is this in? What source did you get the problem? (Olympiad, textbook, site)?
I don't know the answer myself, but the reason I'm asking is that you can get ideas by extrapolating information from the answers to the above questions.
For example if its in say a multi-variable calc book, or an optimization book, these give big hints to solving the problem.