For the part where you're "evaluating" at x, you'll need to work with the functions directly. But the operations on functions work the exact same way: Take the formulas, and do the operations with the polynomials or whatever, instead of which the numbers.
In this case, you'll be multiplying the two polynomials to get the answer.
composition of functions. (I will guess that you mean "F" and "f" to mean the same function, as well as "G" and "g".)