Sometimes it is useful to “undo” the action of a function \(f: X \rightarrow Y\) . If f maps 3 to 5, we might wish to “undo” that by finding a function that takes 5 back to 3. This is most useful when we can undo the action of f on the whole range, not at just one point, because then every element ends up back where it started. We begin the chapter by discussing composition of two functions. This leads naturally to a discussion of the properties a function f must have in order to ensure that f has an inverse. Once we know what the essential properties are, we can (and do) investigate such functions and their inverses further.