A (total) function f from A to B, f: A->B, is a relation from A to B such that for all x ∈ A there is exactly one element in B, f(x) associated with x by a relation f

The subset D ⊆ A of all elements for which f is defined is called the domain of f. In case of a total function D=A. In case of a partial function, D ⊂ A

Let f: A->B(f is partial or total): what is the co-domain?

range(f) = {f(x) |x ∈ A} or The range (image) of f, denoted by range(f), is the set of elements in the co-domain B that are associated with some element of A

when is a function such as f: A->B called injective?

A function f: A->B is called injective (also one-to-one) if it maps distinct elements ofA to distinct elements of B. or for all x, y ∈ A if x ≠y => f(x)≠f(y)

when is a function such as f: A->B called surjective?