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.

2006, Robert L. Causey, Logic, Sets, and Recursion, 2nd Edition, Jones & Bartlett Learning, page 192,
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∈ mathit Img(f,A) iff there is some x in the domain such that f maps x to y.

For example, the codomain of g(X)=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.

Codomain

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