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Image


If f:D->Y is a map (a.k.a. function, transformation, etc.) over a domain D, then the image of f, also called the range of D under f, is defined as the set of all values that f can take as its argument varies over D, i.e.,

 Range(f)=f(D)={f(X):X in D}.

"Image" is a synonym for "range," but "image" is the term preferred in formal mathematical writing.

The notation f([a,b]) denotes the image of the interval [a,b] under the function f. Formally,

 f([a,b])={y: exists x in [a,b] such that f(x)=y}.

See also

Preimage, Range

This entry contributed by John Renze

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Cite this as:

Renze, John. "Image." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/Image.html

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