文档介绍：)(xfy?yxoD一、函数1. 函数的概念定义:Df:R)(?Df??DxxfyyDf???,)()(定义域值域图形:??DxxfyyxC???,)(),(( 一般为曲线)设,R?D函数为特殊的映射:其中机动目录上页下页返回结束2. 函数的特性有界性,单调性,奇偶性,周期性3. 反函数)(:DfDf?设函数为单射,反函数为其逆映射DDff??)(:14. 复合函数给定函数链)(:11DfDf?1)(:DDgDg??则复合函数为])([:DgfDgf??5. . 设函数,1,1,13)(???????xxxxxf????)]([xff1)(,1)(3??xfxf1)(,)(?xfxf0?x??????0,49??xx1)13(3??x10??x1,?xx求.)]([xff解:,13?x机动目录上页下页返回结束xxxff????1211)()(,2)()(1xfxfxx???解:利用函数表示与变量字母的无关的特性.,1xxt??,11tx??代入原方程得,)()(1211tttff????,111uux???,11ux??代入上式得,)()()1(2111uuuuuff?????1,0??xx设其中).(xf求令即即令即画线三式联立1111)(?????xxxxf即xxxxxff)1(2111)()(?????. 下列各组函数是否相同? 为什么? )os2cos()()1(xxf?]1,1[,12)(2????xxx?与??????axaaxxxf,,)()2(??2)(21)(xaxax?????与??????0,0,0)()3(xxxxf)]([)(xffx??与相同相同相同机动目录上页下页返回结束2. 下列各种关系式表示的y是否为x的函数? 为什么?1sin1)1(??xy??],0[,cos,sinmax)2(2???xxxy22,arcsin)3(xuuy???不是40???x,cosx24????x,sinx是不是提示: (2)?y机动目录上页下页返回结束????????0,10,1)()4(33xxxxxf???????0,10,1)()2(xxxf??????1,41,2)()3(xxxf,2xx?xyo421⑶????????1,11,13xx1)1(32????xx,16x??oxy11?⑵0?x1?xR?x3. 下列函数是否为初等函数? 为什么????????0,0,)()1(xxxxxf2x?xy1⑷,0)(,1)]([,)(2????xxxfexfx??且求)(x?????????8,)]5([8,3)(xxffxxxf, 求.)5(,coscsc)sin1(sin22xxxxf???求.)(xf由)(2xe?x??1得,)1ln()(xx???]0,(???x,e?)(f?x2x??][f)(x?4. 解:e)(x?2机动目录上页下页返回结束][f?????????8,)]5([8,3)(xxffxxxf, 求.)5(f解:)5(f)(f?310?)10(f)7(f?][f?)12(f)(f?312?)9(f?6?,coscsc)sin1(sin22xxxxf???求.)(xf解:1sin)(sin2sin1sin12????xxfxx?3)(sin2sin1???xx3)(2???xxf机动目录上页下页返回结束二、连续与间断1. 函数连续的等价形式)()(lim00xfxfxx????)()(,000xfxxfyxxx????????0lim0????yx)()()(000xfxfxf????,0???,0???,0时当???xx有???)()(0xfxf2. 函数间断点第一类间断点第二类间断点可去间断点跳跃间断点无穷间断点振荡间断点机动目录上页下页返回结束