Difference between revisions of "Functions:Forward Image"
(Replaced content with "In mathematics, the image of a function is the set of all output values it may produce. More generally, evaluating a given function <math>f</math> at each element of a gi...") Tag: Replaced |
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In mathematics, the image of a function is the set of all output values it may produce. | In mathematics, the image of a function is the set of all output values it may produce. | ||
| − | More generally, evaluating a given function <math>f</math> at each element of a given subset | + | More generally, evaluating a given function <math>f</math> at each element of a given subset <math>A</math> of its domain produces a set, called the "image of <math>A</math> under (or through) <math>f</math>". Similarly, the inverse image (or preimage) of a given subset <math>B</math> of the codomain of <math>f</math>, is the set of all elements of the domain that map to the members of <math>B</math>. |
Image and inverse image may also be defined for general binary relations, not just functions. | Image and inverse image may also be defined for general binary relations, not just functions. | ||
Revision as of 09:21, 12 October 2021
In mathematics, the image of a function is the set of all output values it may produce.
More generally, evaluating a given function Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f} at each element of a given subset of its domain produces a set, called the "image of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A} under (or through) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f} ". Similarly, the inverse image (or preimage) of a given subset Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle B} of the codomain of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f} , is the set of all elements of the domain that map to the members of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle B} .
Image and inverse image may also be defined for general binary relations, not just functions.
