Relation Between Image And Preimage. The image is the result of performing a transformation and the preimage is the original that you perform the transformation. To tell them apart they will usually be defined separately.
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Perhaps you ve heard of the vertical line test for a function. 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. Well the horizontal line test determines whether a function is injective or not when it can be plotted on the cartesian plane.
In words the image f x of x is the set of all things in b that f sends elements of x to.
More generally evaluating a given function f at each element of a given subset a of its domain produces a set called the image of a under or through f similarly the inverse image or preimage of a given subset b of the codomain of f is the set of all elements of the domain that map to the members. When a function has a unique preimage for every element of the image we say that the function is injective. In mathematics the image of a function is the set of all output values it may produce. For example the square abcd when translated four units right becomes square a b c d.
