<P> Any morphism with a right inverse is an epimorphism, but the converse is not true in general . A right inverse g of a morphism f is called a section of f . A morphism with a right inverse is called a split epimorphism . </P> <P> Any function with domain X and codomain Y can be seen as a left - total and right - unique binary relation between X and Y by identifying it with its function graph . A surjective function with domain X and codomain Y is then a binary relation between X and Y that is right - unique and both left - total and right - total . </P> <P> The cardinality of the domain of a surjective function is greater than or equal to the cardinality of its codomain: If f: X → Y is a surjective function, then X has at least as many elements as Y, in the sense of cardinal numbers . (The proof appeals to the axiom of choice to show that a function g: Y → X satisfying f (g (y)) = y for all y in Y exists . g is easily seen to be injective, thus the formal definition of Y ≤ X is satisfied .) </P> <P> Specifically, if both X and Y are finite with the same number of elements, then f: X → Y is surjective if and only if f is injective . </P>

Explain how the domain and range of a function compare to the domain and range of its inverse