You do such questions by thinking about what "rank" and "nullity" mean. If f:V-->W, then f(V) is some subspace of W. The rank of f is the dimension of that subspace. Of course, the dimension of f(V) cannot be larger than the dimension of V itself.
f.g(U)= f(g(V)). The rank of f.g is the dimension of that space and, as I said, it cannot be larger than the dimension of g(V) which [b]is[b] the rank of g.
If f:V-->W then the nullity of f is the dimension of its "null space"- the subspace of V such that f(v)= V whenever v is in that subspace. In particular, if g(v)= 0, then f(g(v))= f(0)= 0 so the null space of g is a subspace of the null space of f.g. What does that tell you about their dimensions?