The most difficult part of this chapter were the examples at the end of the section. For example, example 9.10 threw me for a loop with showing that the composition was defined. Then I realized that since the input into the next function was a subset of the more or less intended or defined input for the function that that made sense.
Even though it was confusing at first that is my favorite part about this section. Thr functions are like playing frogger. You need to jump from function to function just like lilypads. If you don't go in order it doesnt work. You can't skip from domain to any range you want. But in the example referred to above our jump, or function, landed us in the ballpark that we needed to be allowing us to use the next function. Even though we didn't have every part of that set, the function was prepared to deal with any one element in the larger set B and so it worked for the subset of B
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