Image

In mathematics, the image of a subset of a function's domain under the function is the set of all outputs obtained when the function is evaluated at each element of the subset. The inverse image or preimage of a particular subset S of the codomain of a function is the set of all elements of the domain that map to the members of S. The word "image" is used in three related ways. In these definitions, f : X → Y is a function from set X to set Y. If... more

In mathematics, the image of a subset of a function's domain under the function is the set of all outputs obtained when the function is evaluated at each element of the subset. The inverse image or preimage of a particular subset S of the codomain of a function is the set of all elements of the domain that map to the members of S. The word "image" is used in three related ways. In these definitions, f : X → Y is a function from set X to set Y. If x is a member of X, then f(x) = y (the value of f when applied to x) is the image of x under f. y is alternatively known as the output of f for argument x. The image of a subset A ⊆ X under f is the subset f[A] ⊆ Y defined by (in set-builder notation): When there is no risk of confusion, f[A] is simply written as f(A). This convention is a common one; the intended meaning must be inferred from the context. This makes the image of f a function whose domain is the power set of X (the set of all subsets of X), and whose codomain is the power set... less