We discussed an example of a bijective function from the reals into the reals (Example 4.17 in the textbook), and how to actually prove it is a bijection. We also talked about encoding subsets of [n] with binary n-tuples, and proved the encoding was really a bijection. Remember that to prove there is a unique solution to f(x) = b, one must really prove two things: that there is a solution, and that it is unique. The uniqueness part is also very important.
I also gave the solution to Problem 4.20, which was one of the assigned, but uncollected, problems.