Summary

These notes cover various types of functions, including their definitions, properties, and graphical representations. They are a good resource for understanding functions in mathematics.

Full Transcript

etc 2a3 (()- 4) a (*) 3) z'+3 ()- f 2) 1)Cx)-...

etc 2a3 (()- 4) a (*) 3) z'+3 ()- f 2) 1)Cx)- sin sths Sone )=4 then z-3 wrt dontd aa enenally olested is tion somget cotlonain the ofiswhese oddavnain dntinn hasa uout.Ery xy one selto aked wgnt is each hene wyauts loem selaienip in wstds kunsple endh: óuhput delined 6 )inean mctin 9) Katinal mction 9) tlaaaic mction 13) atet hnteoral nian J9atianal fait wncion 15)venad dd mctin 10) eiie tmction Ke wwesst a jumtin f iü ametion tat the bigetit odes gt Wie nen dimaw in it Aad mase m et Bis wwetible d phas owaim in Bond 'wage mBA f(*)=yG)=x Viot allttias has innene t adwion to hae wwett, element bEB mwst nt hane moe tthan bWe mcion. aEA- egntion wwtt he am njectit dntion element B wut lae a Sustine dmetian Yt is weNosy that the dumion isis one- oMe amd omto to be wele amd e vesa is tuteneting to kw the cowpositinn oa jninamd ita mee hetuw the eleent o the davtain Domain a GD-Range of P(2) Domam of ()=Raneo P) for example : pCadding 8) (Gubatacirg3) " Invevse of adding is subtractin ’ Inverse of multhplicaton is division 10 lecw: Ca)is f then fla)- bamd wt thuina mthe same wamei thesw can he ypoved yf) 11 aist. Sincc both le ouqwal ion fx) ad the wasse Andinns, osth nctons each eleent mthe dowaw A mviht Tld ane to tonlaw (5,4)and (5,), but sawe t component t meoms to hae aiwnee the daman A on to the sant numben Hhe Aange A 46 a unctinn ham Moe the oe, than mae bmevetical le est iiovttal vetical avd wse can wt whethen totina gle 12 13 2z and A 44 ivestile Hh kanctinsnd Covvdinat the endg print tae, the orwnt with cndimats (5,10) ies nthe graph wage the print as oodinaes (8,5). "%a fwnthon to loe wnesse muut be one-to one »A tutcn that unot sne-to one ovea ts enlie domaunmay " haablan bunction, ouhanye the mpud amd outgut not to obtamte 'mweh has an mtrsc

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