Image And Preimage Math. In mathematics the image of a function is the set of all output values it may produce. Roughly speaking you might think of f x as a kind of distorted copy or image of x in b the preimage f 1 y of y is the set of all things in a that f sends into y.
The preimage pi 1 ell consists of two antipodal points x and x in mathbb s n 1 thus f is a discrete two point set mathbb z 2 1 1. As nouns the difference between preimage and image is that preimage is mathematics the set containing exactly every member of the domain of a function such that the member is mapped by the function onto an element of a given subset of the codomain of the function formally of a subset b of the codomain y under a function ƒ the subset of the domain x defined by while image is an optical or other representation of a real object. In addition to finding images preimages of elements we also find images preimages of sets.
The image is the result of performing a transformation and the preimage is the original that you perform the transformation.
Roughly speaking you might think of f x as a kind of distorted copy or image of x in b the preimage f 1 y of y is the set of all things in a that f sends into y. To tell them apart they will usually be defined separately. As nouns the difference between preimage and image is that preimage is mathematics the set containing exactly every member of the domain of a function such that the member is mapped by the function onto an element of a given subset of the codomain of the function formally of a subset b of the codomain y under a function ƒ the subset of the domain x defined by while image is an optical or other representation of a real object. A subseteq f 1 b iff f a subseteq b.