例谈抽象函数解法（abstract the solution to abstract functions）

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1、例谈抽象函数解法（Abstractthesolutiontoabstractfunctions）Mywell-organizeddocumentAbstract:thesolutiontoabstractfunctionsThefunctionisthehotspotoftheannualcollegeentranceexaminationAndtheapplicationofabstractfunctionisoneofthedifficultpointsAnabstractfunctionisafunctionthatdoesnotgiveaspecificfunctionresolut

2、ionorimageButsomepropertiesoralgorithmsoffunctionsatisfactionaregivenSuchfunctiontestscancomprehensivelyexaminestudents'understandingoffunctionconceptsandtheirabilityofalgebraicreasoningandreasoningItcanalsoexaminestudents'understandingandacceptanceofmathematicalsymbollanguageAndunderstandingofgene

3、ralandspecialrelationshipsSothepropositionalfavorInthelastfewyears,thehighexamquestionisconstantlyappearingBecauseabstractfunctionshavesomeabstractionItsnatureishiddenSostudentsaremoreafraidofabstractfunctionsActually,Alargenumberofabstractfunctionsareabstractedfromthebasicfunctionslearnedinmiddles

4、choolWhentheproblemsolvingStartwiththebackgroundofstudyingabstractfunctionsAccordingtothenatureoftheabstractfunctionByanalogy,guessthatitmightbesomebasicfunctionYoucanalwaysfindawaytodothisThisarticlestartswiththisunderstandingInthispaper,somecommontypesofabstractfunctionsandtheirsolutionsarediscus

5、sed1.LinearfunctionalabstractfunctionsLinearfunctionalabstractfunctionsIt'safunctionthatisabstractedbylinearfunctionsThebasictype:f(x+y)=f(x)+f(y)typicalfunction:f(x)=kxSomedatawhicharefrequentlyused:f(0)=f(0+0)=f(0)+f(0)∴f(0)=0F(0)=f(x-x)=f(x)+f(x)∴f(x)=f(x)-Weknowthatf(x+y)=f(x)+f(y).F(4)=16Let's

6、takefofminus2.F(4)=f(2+2)=f(2)+f(2)=16∴8∴f(2)=f(2)=f(2)=8Weknowthatthisisafunctionoff(x)onRF(2)=1,f(x+y)=f(x)+f(y)Theinequality:f(x)+f(x-2)<3Analysis:itisassumedthatf(x)isanabstractfunctionofy=xAndfofxisamonotoneadditionSolution:3=3f(2)=f(2)+f(2)+f(2)=f(6).∴f(x)+f(x2)<3=f(6)∴x+(x-2)<6∴x<4Example3.T

7、hefunctionf(x)isknowntoanyrealnumberxyIhavef(x+y)=f(x)+f(y).AndwhenxBBB00F(x)>0Fofnegative1isminus2IwantfofxintheintervalTherangeofthetopAnalysis:itisknownfromtheproblemsetFunctionfofxisanabstractfunctionSo