I was wondering if someone here could help me with onto and one-to-one composite functions. I get the meanings of one-to-one and onto, but I'm just finding it hard applying them to composite functions. For instance if A,B and C are sets and f:A-B and g:B-C then if f isn't onto then is gof onto or not? Also, how can you prove this if it is true? I would have said it wouldn't be onto but I'm not sure how to prove this. Also, if you use the same sets and g is not one-to-one, then is gof one-to-one or not? I would have said that is wouldn't be one-to-one, but I'm doubting that's correct and I'm unsure of how to prove it. Any help would be much appreciated. Thanks.