Conjunto imagem

A imagem do conjunto X é o conjunto {A,B,D} que é subconjunto de Y.

Função sobrejetora: Neste caso, a imagem do conjunto X é o conjunto Y, porque todos seus valores estão associados a algum elemento do conjunto X.

Em matemática, o conjunto imagem ou campo de valores de uma função $f:X\to Y$ é o conjunto de todos os elementos de $Y$ que são imagem de algum elemento de X.^[1] Costuma ser representado por $\operatorname {I} (f)$ ou $\operatorname {Im} (f).$ Por definição, o conjunto imagem é um subconjunto do contradomínio: $\operatorname {I} (f)\subseteq Y.$

A imagem de um dado elemento $x$ do domínio é o único $y$ do contradomínio associado a ele pela função $f.$ É representada por $f(x).$ Portanto, temos: $\operatorname {I} (f)=\{\,y\in Y\,|\,y=f(x){\text{ para algum }}x\in X\,\}.$ Uma função $f:X\to Y$ , cujo contradomínio é dado por Y e $\operatorname {I} {(f)}=Y$ , isto é, quando o conjunto imagem tem os mesmos elementos do contradomínio, é chamada de sobrejetora. Uma função $f:X\to Y$ , cujo contradomínio é dado por Y e $\operatorname {I} {(f(x_{1}))}\neq \operatorname {I} {(f(x_{2}))}\implies x_{1}\neq x_{2}$ , isto é, quando a imagem de $x_{1}$ é diferente da imagem de $x_{2}$ e que $x_{1}$ é diferente de $x_{2}$ , é chamada de injetora. Se uma função é injetora e $\operatorname {I} {(f(x_{1}))}=\operatorname {I} {(f(x_{2}))}$ , então $x_{1}=x_{2}$ . É bijetora, isto é, sobrejetora e injetora, uma vez que $\operatorname {I} {(f)}=\{\ y\in Y\ |\ \exists !x\in X,f(x)=y\}=Y$ .

Exemplo

Seja a função $g:\mathbb {R} \rightarrow \mathbb {R} ,$ definida por $g(x)=x^{2}.$ A imagem de 2 pela função $g$ é $g(2)=2^{2}=4.$ De maneira análoga, diz-se que as imagens de 6, -6 e 7 pela função $g$ são 36, 36 e 49, respectivamente, o que pode ser representado matematicamente por $g(6)=36,$ $g(-6)=36$ e $g(7)=49.$ O conjunto imagem de $g$ é o conjunto de todos os valores assumidos por $g(x),$ para todo $x\in \mathbb {R} .$ Portanto, $I(g)=\mathbb {R} _{+}.$

Referências

↑ Neto, Aref Antar; Sampaio, José (2009). Conjuntos e funções. 2º grau. 1. Fortaleza: Vestseller. ISBN 978-85-60653-04-1

Ver também

Este artigo sobre matemática é um esboço. Você pode ajudar a Wikipédia expandindo-o.

Read other articles:

ملف:IPAF-2010-Arab-World-ARABIC.jpg

ملخص معلومات الملف الوصف مخطط معلومات بياني للدورة الثالثة (2010) للجائزة العالمية للرواية العربية. المصدر تم تصميم الأيقونة بناء على تصاميم مشتقة من أنظر هنا، ومن أنظر هنا، ومن أنظر هنا. التاريخ 28 مارس، 2017. المنتج عمل شخصي. الإذن(إعادة الاستخدام) أنا مالك الحقوق وأدرجه تحت تر...

Loving v. Virginia

Loving v. Virginia Cour suprême des États-Unis Informations générales Nom complet Richard Perry Loving, Mildred Jeter Loving v. Virginia Soumis 1967 Décidé 12 juin 1967 modifier Loving v. Virginia (« Loving contre l'État de Virginie ») est une décision de la Cour suprême des États-Unis (no 388 U.S. 1), arrêtée le 12 juin 1967. À l'unanimité des neuf juges, elle casse une décision de la Cour suprême de Virginie (en) et déclare comme anticonstitutio...

Stefano Della Santa

Questa voce sull'argomento ciclisti italiani è solo un abbozzo. Contribuisci a migliorarla secondo le convenzioni di Wikipedia. Segui i suggerimenti del progetto di riferimento. Stefano Della Santa Stefano Della Santa in maglia Mapei-Viner nel 1993 Nazionalità Italia Ciclismo Specialità Strada Termine carriera 2000 Carriera Squadre di club 1989 Pepsi Cola1990-1992 Amore & Vita1993Eldor-Viner1993-1996 Mapei1997 Mercatone Uno1998 Ros Mary1999 Ami...

Remain in Mexico

U.S. federal immigration policy Remain in Mexico (officially Migrant Protection Protocols) is a United States immigration policy originally implemented in January 2019 under the administration of President Donald Trump, affecting immigration across the border with Mexico. Administered by the Department of Homeland Security, it requires migrants seeking asylum to remain in Mexico until their US immigration court date. The policy was initially ended by the Biden administration, and after some l...

Downtown Miami Historic District

Historic district in Florida, United States United States historic placeDowntown Miami Historic DistrictU.S. National Register of Historic PlacesU.S. Historic district Downtown Miami skyline in the early 1930sShow map of MiamiShow map of FloridaShow map of the United StatesLocationDowntown, Miami, FloridaCoordinates25°46′28.8546″N 80°11′30.8652″W / 25.774681833°N 80.191907000°W / 25.774681833; -80.191907000Architectural styleModerne, Classical Revival,...

Central Scotland (Scottish Parliament electoral region)

Electoral region of the Scottish Parliament For other uses, see Central Scotland (disambiguation). Central Scotlandelectoral regionfor the Scottish ParliamentCentral Scotland shown within ScotlandPopulation669,424 (2019)[1]Current electoral regionCreated1999MSPsScottish National Party 9Conservative 3Labour 3Green 1Council areasFalkirkNorth LanarkshireSouth Lanarkshire (part)ConstituenciesAirdrie and ShottsCoatbridge and ChrystonCumbernauld and KilsythEast KilbrideFalkirk EastFalkirk W...

西維吉尼亞州

西維珍尼亞美國联邦州State of West Virginia 州旗州徽綽號：豪华之州地图中高亮部分为西維珍尼亞坐标：37°10'N－40°40'N, 77°40'W－82°40'W国家美國加入聯邦1863年6月20日（第35个加入联邦）首府（最大城市）查爾斯頓政府 • 州长（英语：List of Governors of {{{Name}}}]]） • 副州长（英语：List of lieutenant governors of {{{Name}}}]]）吉姆·賈斯蒂斯（R）米奇·卡邁克爾（...

世界政區索引

此條目可能包含不适用或被曲解的引用资料，部分内容的准确性无法被证實。 (2023年1月5日)请协助校核其中的错误以改善这篇条目。详情请参见条目的讨论页。各国相关主題列表索引国内生产总值石油储量国防预算武装部队（军事）官方语言人口統計人口密度生育率出生率死亡率自杀率谋杀率失业率储蓄率识字率出口额进口额煤产量发电量监禁率死刑国债 ...

ヨハネス12世 (ローマ教皇)

ヨハネス12世第130代ローマ教皇教皇就任 955年12月16日教皇離任 964年5月14日先代アガペトゥス2世次代レオ8世個人情報出生 937年スポレート公国（中部イタリア）スポレート死去 964年5月14日教皇領、ローマ原国籍スポレート公国親父アルベリーコ2世（スポレート公）、母アルダその他のヨハネステンプレートを表示ヨハネス12世（Ioannes XII、937年 - 964年5月14日）は、ロ...

كأس العالم 1998 المجموعة ج

يفتقر محتوى هذه المقالة إلى الاستشهاد بمصادر. فضلاً، ساهم في تطوير هذه المقالة من خلال إضافة مصادر موثوق بها. أي معلومات غير موثقة يمكن التشكيك بها وإزالتها. (ديسمبر 2018) كأس العالم 1998 المجموعة جمعلومات عامةجزء من كأس العالم 1998 فئة المنافسة كرة القدم للرجال الرياضة كرة القدم...

CoopVoce

CoopVoce Scheda SIM CoopVoce CoopVoce è l'operatore di telefonia mobile di Coop, il primo MVNO lanciato in Italia. Operativo dal 1º giugno 2007 come ESP MVNO, dopo una fase sperimentale durata circa tre mesi, è nato dall'accordo tra la società Coop e TIM del quale utilizza la rete GSM/UMTS/LTE per l'erogazione del servizio. Nel 2020 diventa Full MVNO.[1][2] Dal 3 Marzo 2022 l'operatore rende disponibili le eSIM sia per i nuovi clienti che per i già clienti.[3] Vie...

رمسيس السادس

رمسيس السادس معلومات شخصية تاريخ الميلاد القرن 12 ق.م تاريخ الوفاة سنة 1136 ق م مكان الدفن مقبرة 9 مواطنة مصر القديمة الزوجة نوب خسبد الأولاد رمسيس السابع الأب رمسيس الثالث الأم إست تاحمجرت إخوة وأخوات دوات إنت أوبت، ورمسيس الرابع، ورمسيس الث�...

The Good Guys and the Bad Guys

1969 film by Burt Kennedy This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: The Good Guys and the Bad Guys – news · newspapers · books · scholar · JSTOR (February 2016) (Learn how and when to remove this message) The Good Guys and the Bad GuysFilm posterDirected byBurt KennedyWritten byRonald M. CohenDennis Sh...

Daniel Zampieri

Italian racing driver Daniel ZampieriZampieri at the 2011 Nürburgring World series by Renault roundNationality ItalianBorn (1990-05-22) 22 May 1990 (age 34)Rome, ItalyInternational GT Open careerDebut season2012Current teamAntonelli MotorsportRacing licence FIA GoldCar number6Former teamsKessel Racing, SMP Racing Russian BearsStarts48Wins4Poles4Fastest laps5Best finish1st in 2014Previous series2010–122009–1020092006–082006–082006–07World Series by RenaultGP2 Asia SeriesItalian...

Kubotan

This article includes a list of references, related reading, or external links, but its sources remain unclear because it lacks inline citations. Please help improve this article by introducing more precise citations. (January 2024) (Learn how and when to remove this message) This article may rely excessively on sources too closely associated with the subject, potentially preventing the article from being verifiable and neutral. Please help improve it by replacing them with more appropriate c...

North American F-107

North American F-107 adalah jet fighter supersonik bermesin tunggal diproduksi dalam jumlah kecil oleh North American Aviation AS di akhir tahun lima puluhan . Pengembangan sebelumnya berburu North American F-100 Super Sabre, dirancang untuk menjawab spesifik yang dikeluarkan oleh Angkatan Udara Amerika Serikat, tetapi dalam evaluasi akhir lebih disukai ke Republik F-105 Thunderchief dan perkembangannya terganggu. Hanya tiga salinan dibuat, bagaimanapun, masa kerja singkat, prototipe # 1 dan...

PAMELA detector

For other uses, see PAMELA (disambiguation). PAMELA Organization PAMELA group Mission Type Cosmic Ray Host Satellite Resurs DK1 Launch 15 June 2006 Launch vehicle Soyuz-FG Launch site Baikonur Cosmodrome Mission duration 3 years (planned), 9 years, 7 months and 23 days (achieved) Mission end 7 February 2016 Mass 470 kg Max length 1300 mm Power consumption 335 Watts Webpage PAMELA homepage Orbital elements (Resurs DK1) Inclination 70 degrees Orbit quasi-polar elli...

Angelus

Christian devotion This article is about the religious devotion. For other uses, see Angelus (disambiguation). The Angelus (1857–1859) by Jean-François Millet Part of a series on theMariologyof the Catholic ChurchImmaculate Conception by Bartolomé Esteban Murillo (c. 1675) Overview Prayers Antiphons Titles Hymns to Mary Devotional practices Saints Societies Consecrations and entrustments Veneration Titles of Mary Theotokos (Mother of God) Mediatrix Mother of the Church Our Lady of G...

Eljero Elia

Dutch footballer (born 1987) Eljero Elia Elia in 2012Personal informationFull name Eljero George Rinaldo Elia[1]Date of birth (1987-02-13) 13 February 1987 (age 37)Place of birth Leidschendam-Voorburg, NetherlandsHeight 1.76 m (5 ft 9 in)[2]Position(s) WingerYouth career SV Voorburg TONEGIDO1996–2000 ADO Den Haag2000–2002 Ajax2002–2004 ADO Den HaagSenior career*Years Team Apps (Gls)2004–2007 ADO Den Haag 59 (6)2007–2009 Twente 64 (11)2009–2011 H...

Incidence (graph)

An incidence graph is a Levi graph. This article includes a list of references, related reading, or external links, but its sources remain unclear because it lacks inline citations. Please help improve this article by introducing more precise citations. (February 2023) (Learn how and when to remove this message) This article relies largely or entirely on a single source. Relevant discussion may be found on the talk page. Please help improve this article by introducing citations to additional ...