The problem is:
Suppose that f:A-->B, g:B-->C are functions. In the following cases, answer yes or no. If your answer is yes, prove it. If it is no, give a counterexample and say what additional hypotheses are needed to make the statement true, then prove.
1. if gof is 1-1, must f be 1-1?
2. if gof is 1-1, must g be 1-1?
3. if gof is onto, must f be onto?
4. if gof is onto, must g be onto?
I'm fine with 1 and 4, and for 2, I think the answer is yes, but I'm not sure how to go about proving it. I understand it, and I could explain it in English (if g isn't 1-1, then two elements in B go to the same element in C, and the two elements in A go to the two elements in B, which go to the same element in C) but I'm not sure how to say it in a proof. For 3, I'm just confused. The element that is not in the range of f could still be in the domain of g, so I think I have to say no, and add something to it, but I'm not sure what.