In mathematics , the domain of a function is the set of inputs accepted by the function . It is sometimes denoted by dom ( f ) {\displaystyle \operatorname {dom} (f)} or dom f {\displaystyle \operatorname {dom} f} , where f is the function. In layman's terms, the domain of a function can generally be thought of as "what x can be".
23-525: (Redirected from DOM ) [REDACTED] Look up dom , Dom , or DOM in Wiktionary, the free dictionary. Dom or DOM may refer to: People and fictional characters [ edit ] Dom (given name) , including fictional characters Dom (surname) Dom La Nena (born 1989), stage name of Brazilian-born cellist, singer and songwriter Dominique Pinto Dom people , an ethnic group in
46-445: A small form-factor pluggable transceiver 2,5-Dimethoxy-4-methylamphetamine or DOM/STP, a psychedelic phenethylamine Dioctyl maleate , a chemical compound used in the manufacture of surfactants Directed ortho metalation , a chemical reaction mechanism Disk-on-a-module , an alternative to traditional computer hard disk drives Dissolved organic matter , a central nutrient in aquatic ecosystems Document Object Model ,
69-445: A small form-factor pluggable transceiver 2,5-Dimethoxy-4-methylamphetamine or DOM/STP, a psychedelic phenethylamine Dioctyl maleate , a chemical compound used in the manufacture of surfactants Directed ortho metalation , a chemical reaction mechanism Disk-on-a-module , an alternative to traditional computer hard disk drives Dissolved organic matter , a central nutrient in aquatic ecosystems Document Object Model ,
92-560: A cross-platform and language-independent application programming interface dom {\displaystyle \operatorname {dom} } , the domain of a function Other uses [ edit ] Dom (church) , cognate with the Italian term duomo , meaning a collegiate church or cathedral Dom (title) , a title of respect, derived from the Latin Dominus Deo optimo maximo , abbreviated D.O.M., Latin for "to
115-437: A cross-platform and language-independent application programming interface dom {\displaystyle \operatorname {dom} } , the domain of a function Other uses [ edit ] Dom (church) , cognate with the Italian term duomo , meaning a collegiate church or cathedral Dom (title) , a title of respect, derived from the Latin Dominus Deo optimo maximo , abbreviated D.O.M., Latin for "to
138-671: A linguistic feature Dom language , spoken in Papua New Guinea Places [ edit ] Dom (mountain) , Switzerland, the third highest mountain in the Alps Overseas department , ( Département d'outre-mer ), a department of France that is outside metropolitan France Dóm Square , a large town square in Szeged, Hungary Dominican Republic (ISO 3166-1 country code) Douglas–Charles Airport (IATA airport code), Dominica Dominion of Melchizedek ,
161-479: A linguistic feature Dom language , spoken in Papua New Guinea Places [ edit ] Dom (mountain) , Switzerland, the third highest mountain in the Alps Overseas department , ( Département d'outre-mer ), a department of France that is outside metropolitan France Dóm Square , a large town square in Szeged, Hungary Dominican Republic (ISO 3166-1 country code) Douglas–Charles Airport (IATA airport code), Dominica Dominion of Melchizedek ,
184-640: A micronation known largely for facilitating large scale banking fraud in many parts of the world Buildings [ edit ] Dom Tower of Utrecht , a tower in Utrecht, the Netherlands Dom-Hotel , a five-star hotel in Cologne, Germany D.O.M. (restaurant) , a restaurant in São Paulo, Brazil Science and technology [ edit ] Digital optical monitoring, a function in
207-400: A micronation known largely for facilitating large scale banking fraud in many parts of the world Buildings [ edit ] Dom Tower of Utrecht , a tower in Utrecht, the Netherlands Dom-Hotel , a five-star hotel in Cologne, Germany D.O.M. (restaurant) , a restaurant in São Paulo, Brazil Science and technology [ edit ] Digital optical monitoring, a function in
230-482: A partial function is called simply a function , and its natural domain is called simply its domain . The term domain is also commonly used in a different sense in mathematical analysis : a domain is a non-empty connected open set in a topological space . In particular, in real and complex analysis , a domain is a non-empty connected open subset of the real coordinate space R n {\displaystyle \mathbb {R} ^{n}} or
253-432: A problem is posed, making it both an analysis-style domain and also the domain of the unknown function(s) sought. For example, it is sometimes convenient in set theory to permit the domain of a function to be a proper class X , in which case there is formally no such thing as a triple ( X , Y , G ) . With such a definition, functions do not have a domain, although some authors still use it informally after introducing
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#1732765407998276-576: Is called the codomain : the set to which all outputs must belong. The set of specific outputs the function assigns to elements of X is called its range or image . The image of f is a subset of Y , shown as the yellow oval in the accompanying diagram. Any function can be restricted to a subset of its domain. The restriction of f : X → Y {\displaystyle f\colon X\to Y} to A {\displaystyle A} , where A ⊆ X {\displaystyle A\subseteq X} ,
299-553: Is different from Wikidata All article disambiguation pages All disambiguation pages dom [REDACTED] Look up dom , Dom , or DOM in Wiktionary, the free dictionary. Dom or DOM may refer to: People and fictional characters [ edit ] Dom (given name) , including fictional characters Dom (surname) Dom La Nena (born 1989), stage name of Brazilian-born cellist, singer and songwriter Dominique Pinto Dom people , an ethnic group in
322-407: Is different from Wikidata All article disambiguation pages All disambiguation pages Domain of a function More precisely, given a function f : X → Y {\displaystyle f\colon X\to Y} , the domain of f is X . In modern mathematical language, the domain is part of the definition of a function rather than a property of it. In
345-471: Is written as f | A : A → Y {\displaystyle \left.f\right|_{A}\colon A\to Y} . If a real function f is given by a formula, it may be not defined for some values of the variable. In this case, it is a partial function , and the set of real numbers on which the formula can be evaluated to a real number is called the natural domain or domain of definition of f . In many contexts,
368-482: The complex coordinate space C n . {\displaystyle \mathbb {C} ^{n}.} Sometimes such a domain is used as the domain of a function, although functions may be defined on more general sets. The two concepts are sometimes conflated as in, for example, the study of partial differential equations : in that case, a domain is the open connected subset of R n {\displaystyle \mathbb {R} ^{n}} where
391-608: The Greatest and Best God", originally Jove, later the Christian God Dóm , Old English word meaning "judgment", "law"; see Anglo-Saxon law Days on market , how many days since a piece of real estate was listed for sale Drawn-over-mandrel, a class of manufactured tubing Dominant partner, in BDSM See also [ edit ] Doma (disambiguation) Dom Dom (disambiguation) Topics referred to by
414-429: The Greatest and Best God", originally Jove, later the Christian God Dóm , Old English word meaning "judgment", "law"; see Anglo-Saxon law Days on market , how many days since a piece of real estate was listed for sale Drawn-over-mandrel, a class of manufactured tubing Dominant partner, in BDSM See also [ edit ] Doma (disambiguation) Dom Dom (disambiguation) Topics referred to by
437-564: The Middle East and North Africa Dom (caste) or Domba, an ethnic group in India Arts and entertainment [ edit ] Dom (film) , a 1958 Polish film DOM (album) , a 2012 album by German singer Joachim Witt DOM (band) , a pop/electronic solo musical project by Dominic Cournoyer "Dom", a song by Doda (featuring Bedoes) from Aquaria , 2022 Linguistics [ edit ] Differential object marking ,
460-445: The Middle East and North Africa Dom (caste) or Domba, an ethnic group in India Arts and entertainment [ edit ] Dom (film) , a 1958 Polish film DOM (album) , a 2012 album by German singer Joachim Witt DOM (band) , a pop/electronic solo musical project by Dominic Cournoyer "Dom", a song by Doda (featuring Bedoes) from Aquaria , 2022 Linguistics [ edit ] Differential object marking ,
483-442: The same term [REDACTED] This disambiguation page lists articles associated with the title Dom . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Dom&oldid=1227065953 " Categories : Disambiguation pages Place name disambiguation pages Hidden categories: Short description
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#1732765407998506-442: The same term [REDACTED] This disambiguation page lists articles associated with the title Dom . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Dom&oldid=1227065953 " Categories : Disambiguation pages Place name disambiguation pages Hidden categories: Short description
529-463: The special case that X and Y are both sets of real numbers , the function f can be graphed in the Cartesian coordinate system . In this case, the domain is represented on the x -axis of the graph, as the projection of the graph of the function onto the x -axis. For a function f : X → Y {\displaystyle f\colon X\to Y} , the set Y
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