Difference between revisions of "Range of values"
From Encyclopedia of Mathematics
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| − | ''of a function, set of values of a function'' | + | {{TEX|done}} |
| + | ''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 | + | 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]]. | ||
Latest revision as of 21:17, 18 December 2014
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://encyclopediaofmath.org/index.php?title=Range_of_values&oldid=12364
Range of values. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Range_of_values&oldid=12364
This article was adapted from an original article by L.D. Kudryavtsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article