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Domain and Co-domain of a Function

Let A and B be two nonempty sets. A function f from a set A to set B is a rule that assigns to each element x of A one and one only one element y of B. We call y image of x under f and denote it by f(x). x is called the preimage of y under f. The domain of f is the set A and the co-domain of f is the set B. See Figure 1

We may use an arrow diagram (figure 2) to show the correspondence between the elements of the domain and co-domain.

We denote the function f from A to B by f: A B.

Figure 1

Figure 2

Figure 3

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