You don't provide the instructions for this problem, leaving it up to me to guess what you might want.
Note that g(x) should be written as g(x) = (x-2)^2, whereas f(x) = g(x) + 3 (as presented).
If we let g(x) be the input to f(x), we get the "composition" of g and f:
f(x) = g(x) + 3 = (x-2)^2 + 3. You could leave the answer as is or you could expand (x-2)^2: f(x) = x^2 - 4x + 4 + 3 (and so on).