Imibuzo Eyisibonelo Exoxa Ngemisebenzi Nemisebenzi Engeyona Imisebenzi: Ukuqonda Imiqondo Eyisisekelo
Isingeniso
Kumathematika, ikakhulukazi ku-algebra, umqondo womsebenzi ungomunye wemisebenzi eyisisekelo nebaluleke kakhulu. Imisebenzi isenza siqonde ubudlelwano phakathi kwamasethi amabili ngendlela ehlelekile kakhulu. Ukuze siqonde umsebenzi, sidinga kuqala ukuqonda incazelo yawo kanye nezici zawo. Ngakho-ke, lesi sihloko sizobuyekeza izinkinga zezibonelo futhi sixoxe ngemisebenzi kanye nengeyona imisebenzi. Lokhu kuzosisiza sithuthukise ukuqonda okujulile kwalesi sihloko.
Incazelo Yomsebenzi Nokungasebenzi
Ake siqale ngokuqonda incazelo yomsebenzi. Kumathematika, umsebenzi ungachazwa njengobudlelwano obuhlanganisa into ngayinye yesethi yesizinda nento eyodwa yesethi yesizinda. Ngamanye amazwi, ngento ngayinye kusethi yesizinda, kunento eyodwa ehambisanayo kusethi yesizinda.
Izibonelo Zobudlelwano Obuyimisebenzi:
– Isethi A = {1, 2, 3}
– Isethi B = {4, 5, 6}
– Ubuhlobo R = {(1, 4), (2, 5), (3, 6)}
Ubudlelwano R buwumsebenzi ngoba isici ngasinye sesethi A sibhangqiwe nesici esisodwa kuphela sesethi B.
Ukungasebenzi kuwubuhlobo obungahlangabezani nalezi zindinganiso, okungukuthi kukhona okungenani into eyodwa esifundeni sokuqala ebhangqwe nezinto ezingaphezu kweyodwa esifundeni somphumela.
Izibonelo Zobudlelwano obungeyona Imisebenzi:
– Isethi C = {1, 2, 3}
– Isethi D = {4, 5, 6}
– Ubuhlobo S = {(1, 4), (1, 5), (2, 6)}
Ubudlelwano u-S akuwona umsebenzi ngoba isici '1' kusethi C sibhangqiwe nezinto ezimbili kusethi D (okungukuthi u-4 no-5).
Imibuzo Eyisibonelo Nengxoxo
Ukuze sijulise ukuqonda kwethu imisebenzi kanye nengeyona imisebenzi, ake sibheke eminye imibuzo eyisibonelo kanye nezingxoxo zayo.
Isibonelo Umbuzo 1: Ukunquma Imisebenzi
Uma sinikezwe isethi X = {a, b, c, d} kanye nesethi Y = {1, 2, 3, 4}, ingabe ubudlelwano buchazwa kanje umsebenzi?
– R = {(a, 1), (b, 2), (c, 3), (d, 4)}
Ingxoxo:
Ake sihlole into ngayinye kusethi X:
– 'a' ihambisana no-'1'
– 'b' ihambisana no-'2'
– 'c' kuhlanganiswe no-'3'
– 'd' kuhlanganiswe no-'4'
Njengoba into ngayinye esethiweni X ihambisana nento eyodwa ncamashi esethiweni Y, ubudlelwano R buyi-function.
Isibonelo Umbuzo 2: Ukuhlonza Imisebenzi noma Imisebenzi Engeyona Imisebenzi
Uma unikezwe isethi P = {u, v, w} kanye nesethi Q = {5, 6, 7}. Nquma ukuthi ubudlelwano obulandelayo buyi-function:
– S = {(u, 5), (v, 6), (u, 7)}
Ingxoxo:
Ake sihlole isici ngasinye kusethi P:
– 'u' kuhlanganiswe no-'5'
– 'v' kuhlanganiswe no-'6'
– 'u' ihambisana no-'7'
Njengoba i-element 'u' kusethi P ihambisana ne-element engaphezu kweyodwa kusethi Q, ubudlelwano u-S abuyona i-function.
Isibonelo Umbuzo 3: Imisebenzi Yokudweba Evela Kumagrafu
Uma unikezwe igrafu yobudlelwano endizeni yokuxhumanisa, nquma ukuthi ngabe ngumsebenzi noma cha. Igrafu ikhombisa amaphuzu alandelayo:
– (1, 2)
– (2, 4)
– (3, 6)
– (4, 8)
– (5, 10)
Ingxoxo:
Iphuzu ngalinye kugrafu linepheya lefomu (x, y), okubonisa ukuthi ngenani ngalinye elinikeziwe lika-x kukhona inani elilodwa lika-y elihlotshaniswa nalo. Njengoba isici ngasinye kusizinda sibhangqiwe nesici esisodwa kusizinda, igrafu enikeziwe iyigrafu yomsebenzi.
Isibonelo Inkinga 4: Imisebenzi Efomini Yesilinganiselo
Nquma ukuthi i-equation u-y = x² iwumsebenzi yini uma isizinda esinikeziwe siyizinombolo zangempela zonke.
Ingxoxo:
Sidinga ukuhlola ukuthi inani ngalinye le-x kusizinda linenani elilodwa le-y elihlobene nalo. Faka amanye amanani e-x esikhundleni sawo:
– Uma u-x = 1, khona-ke u-y = 1² = 1
– Uma u-x = 2, khona-ke u-y = 2² = 4
– Uma u-x = -1, khona-ke u-y = (-1)² = 1
Kungabonakala ukuthi ngenani ngalinye elikhethiwe lika-x, kunenani elilodwa elihlobene lika-y. Ngakho-ke, u-y = x² umsebenzi.
Isibonelo Umbuzo 5: Imisebenzi enemisebenzi ephambene
Ake u-f(x) abe umsebenzi ochazwe ngu-f: x → x + 3. Thola okuphambene nalo msebenzi, uma ukhona.
Ingxoxo:
Uma u-f: x → x + 3, sidinga ukuthola umsebenzi u-g ofana nokuthi u-f(g(x)) = x kanye no-g(f(x)) = x. Siqala ngesibalo:
– y = x + 3
Ukuze sithole okuphambene, sihlukanisa u-x:
– x = y – 3
Ngakho-ke, umsebenzi ophambene ngu-g(y) = y – 3.
Ngakho-ke, okuphambene nomsebenzi f(x) = x + 3 ngu-f⁻¹(x) = x – 3.
Isiphetho
Kusukela engxoxweni engenhla, sibone izibonelo eziningana zezinkinga ezihilela imisebenzi kanye ne-non-functions, kanye nezincazelo zazo. Umqondo womsebenzi usifundisa ukuthi isici ngasinye sesethi yesizinda kumele sihambisane nesici esisodwa sesethi ye-codomain. Ukuhlonza imisebenzi kumagrafu kanye nezibalo nakho kuyindlela ewusizo yokunquma uhlobo lobuhlobo. Ngokuzijwayeza lezi zinhlobo zezinkinga, sizojwayelana kakhudlwana futhi siqonde kangcono imiqondo eyisisekelo yemisebenzi kanye ne-non-functions, okuyizisekelo ezibalulekile ku-algebra kanye nokunye ukuhlaziywa kwezibalo.
