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Range of values

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of a function, set of values of a function, image of a function

The set of all elements which a given function puts into correspondence with the elements of its domain of definition; that is, if $f : X \rightarrow Y$, then the set of values of $f$ is the set $Y_f$ of all $y \in Y$ for which there exists an $x \in X$ with $f(x) = y$. Thus, the range of values of a function is the image of its domain of definition, $Y_f = f(X)$.

See also Image of a morphism.

How to Cite This Entry:
Range of values. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Range_of_values&oldid=35688
This article was adapted from an original article by L.D. Kudryavtsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article