Search results
Results From The WOW.Com Content Network
The term range is sometimes ambiguously used to refer to either the codomain or the image of a function. A codomain is part of a function f if f is defined as a triple (X, Y, G) where X is called the domain of f, Y its codomain, and G its graph. [1] The set of all elements of the form f(x), where x ranges over the elements of the domain X, is ...
Sometimes "range" refers to the image and sometimes to the codomain. 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.
The image of a function is the image of its entire domain, also known as the range of the function. [3] This last usage should be avoided because the word "range" is also commonly used to mean the codomain of f . {\displaystyle f.}
The image under f of an element x of the domain X is f(x). [6] If A is any subset of X, then the image of A under f, denoted f(A), is the subset of the codomain Y consisting of all images of elements of A, [6] that is, = {()}. The image of f is the image of the whole domain, that is, f(X). [17]
For a function :, the set Y is called the codomain: the set to which all outputs must belong. The set of specific outputs the function assigns to elements of X is called its range or image. The image of f is a subset of Y, shown as the yellow oval in the accompanying diagram.
A non-surjective function from domain X to codomain Y. The smaller yellow oval inside Y is the image (also called range) of f. This function is not surjective, because the image does not fill the whole codomain.
These properties concern the domain, the codomain and the image of functions. Injective function: has a distinct value for each distinct input. Also called an injection or, sometimes, one-to-one function. In other words, every element of the function's codomain is the image of at most one element of its domain.
The codomain of definition, active codomain, [2] image or range of is the set of all such that for at least one . The field of is the union of its domain of definition and its codomain of definition. [9] [10] [11]