Suppose that U is a simply-connected open domain in C and assume
that are one-to-one and onto maps which are holomorphic mappings with the property that f' and g' are non-zero for all points of
U. Prove that if for i = 1, 2 and then f = g.
I am not sure where to start on this one. I know that if f and g are equal on a set which is not discrete then they are the same, but in this case the set is just two elements. I'm not sure what piece of the puzzle I am missing -- any help would be appreciated.