These are potential proofs for the discrete math exam on Tuesday. I haven't been able to find proofs online. I have senioritis, and I'm graduating in a few weeks. Is a proof by contraposition the best way to prove this? If you assume h is not a function or g is not a function, then that would imply that h ∪ g is not a function. I understand why the domains have to be disjoint. You could run into a problem where an element that appears in both domains is not well-defined.