We discussed some common mistakes in HW 4. I also gave two different ways to solve Problem 4.21 in the current homework. We then went on to discuss function composition, and Problem 4.9 .
It was asked what methods there are to prove a function is not surjective. There is no catch-all method, what you should do really depends on the structure of your problem. Later on, we might discuss diagonalization, which is a useful method to show e.g. that there is no surjection from the natural numbers into the reals.