information:highlighting, information:classification
In mathematics, the range of a function may refer to either of two closely related concepts: the codomain of the function, or
the image of the function. In some cases the codomain and the image of a function are the same set; such a function is called surjective or onto. For any non-surjective function f : X → Y , the codomain Y and the image Y ~ are different; however, a new function can be defined with the original function's image as its codomain, f ~ : X → Y ~ where f ~ = f . This new function is surjective.