Codomain

Definition 2.5. A function is onto if each element of the codomain has at least one element of the domain assigned to it. In other words, a function is onto if the range equals the codomain.

Once we have described f as a function from A to B, by convention we will call B the codomain, even though other sets, of which B is a subset, could have been used.[…]If y is an element of the codomain, then y#92;in#92;mathit#123;Img#125;(f,A) iff there is some x in the domain such that f maps x to y.

For example, the codomain of g(X)#61;X³ consists of all real numbers. A function links each element in its domain to some element in its codomain. Each domain element is linked to exactly one codomain element.