复合函数(知识点总结例题分类讲解).pdf

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复合函数(知识点总结例题分类讲解).pdf

名师推荐精心整理学习必备复合函数的定义域和解析式以及单调性【复合函数相关知识】1、复合函数的定义如果y是u的函数，u又是x的函数，即()yf u，()ug x，那么y关于x的函数()yf g x叫做函数()yf u（外函数）和()ug x（内函数）的复合函数，其中u是中间变量，自变量为x函数值为y。例如：函数212xy是由2uy和21ux复合而成立。说明：复合函数的定义域，就是复合函数()yf g x中 x的取值范围。x称为直接变量，u 称为中间变量，u 的取值范围即为()g x的值域。)(xgf与)(xfg表示不同的复合函数。2求有关复合函数的定义域已知)(xf的定义域为)(ba,，求)(xgf的定义域的方法：已知)(xf的定义域为)(ba,，求)(xgf的定义域。实际上是已知中间变量的u 的取值范围，即)(bau,，)()(baxg,。通过解不等式bxga)(求得 x的范围，即为)(xgf的定义域。已知)(xgf的定义域为)(ba，求)(xf的定义域的方法：若已知)(xgf的定义域为)(ba，求)(xf的定义域。实际上是已知直接变量x的取值范围，即)(bax，。先利用bxa求得)(xg的范围，则)(xg的范围即是)(xf的定义域。3求有关复合函数的解析式已知)(xf求复合函数)(xgf的解析式，直接把)(xf中的x换成)(xg即可。已知)(xgf求)(xf的常用方法有：配凑法和换元法。配凑法：就是在)(xgf中把关于变量x的表达式先凑成)(xg整体的表达式，再直接把)(xg换成x而得)(xf。换元法：就是先设txg)(，从中解出x（即用t表示x），再把x（关于t的式子）直接代入)(xgf中消去x得到)(tf，最后把)(tf中的t直接换成x即得)(xf。学习资料总结-名师归纳欢迎下载-欢迎下载名师归纳-第 1 页，共 6 页 -名师推荐精心整理学习必备4.求复合函数的单调性若)(xgu)(xfy则)(xgfy增函数增函数增函数减函数减函数增函数增函数减函数减函数减函数增函数减函数即“同增异减”法则5.复合函数的奇偶性一偶则偶，同奇则奇【例题讲解】一、复合函数定义域解析式例 1 设函数53)(,32)(xxgxxf，求)(),(xfgxgf例 2 已知xxxf2)12(2，求)122(f例 3 已知,1)(2xxf求)1(xf；已知1)1()1(2xxf，求)(xf例 4 若函数)(xf的定义域是 0，1，求)21(xf的定义域；若)12(xf的定义域是-1，1，求函数)(xf的定义域；已知)3(xf定义域是5,4，求)32(xf定义域例 5 已知xxxf1)1(，求)(xf；已知221)1(xxxxf，求)1(xf例 6 已知)(xf是一次函数，满足172)1(2)1(3xxfxf，求)(xf；学习资料总结-名师归纳欢迎下载-欢迎下载名师归纳-第 2 页，共 6 页 -文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 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ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8名师推荐精心整理学习必备已知xxfxf4)1(2)(3，求)(xf二、复合函数单调性及其值域初等函数复合求单调区间与值域例 1 已知函数22513xxy，求其单调区间及值域。变式练习 1 1.求函数)(xf=2215.0 xx的单调区间及值域2.求函数523421xxy的单调区间和值域.例 2求)(xf=2-4-5xx的单调区间及值域变式练习 2 求函数 f(x)=212x的单调区间及值域例 3求211221(log)log52yxx在区间 2,4上的最大值和最小值变式练习 3 学习资料总结-名师归纳欢迎下载-欢迎下载名师归纳-第 3 页，共 6 页 -文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 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求函数)2(log2xaaaxy的值域。变式练习 41.讨论函数)1(logxaay的单调性其中0a，且1a根据复合函数单调性或值域求参数取值范围例 6 设函数)12lg()(2xaxxf，若)(xf的值域为 R，求实数的取值范围例7 已知)2(logaxya在区间10,上时减函数，求 a 的取值范围.例8 若函数)3(log2axxya在区间21(a,上为减函数，求实数a的取值范围.学习资料总结-名师归纳欢迎下载-欢迎下载名师归纳-第 4 页，共 6 页 -文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8名师推荐精心整理学习必备变式练习 5 已知函数122axxy在区间3,上是增函数,求a的范围.解:令12axxu,则原函数是由12axxu与uy2复合而成.原函数在区间3,上是增函数,而外层函数uy2始终是增函数,则易知内层函数12axxu在区间3,上也是增函数.而实质上原函数的最大单调增区间是2,a,由3,2,a得32a,即6a.【过关检测】1.（1）)(xf452xx;2）5)21(4)41()(xxxg2.求下列函数的单调递增区间：（1）22621xxy;(2)622xxy.3.已知函数)10(log)(aaxxfa,，如果对于任意)3,xx 都有1)(xf成立，试求a的取值范围.4.已知函数)(log)(2aaxxxfaf（x）=log2(x2-ax-a)在区间31,(上是单调递减函数.求实数a的取值范围.5 求函数)32(log125.0 xxy的单调区间学习资料总结-名师归纳欢迎下载-欢迎下载名师归纳-第 5 页，共 6 页 -文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8名师推荐精心整理学习必备【考试链接】1.（2008 山东临沂模拟理，5 分）若1a，且yaxaayaxloglog，则x与y之间的大小关系是（）A0yxB0yxC0 xyD无法确定2.函数|1|lnxeyx的图象大致是（）3（2008 江苏南通模拟，5 分）设xxfalog)(（0a且1a），若1)()()(21nxfxfxf（Rxi，ni,2,1），则)()()(33231nxfxfxf的值等于 _。4（2008 海南海口模拟文、理，5 分）若函数 y=log2（kx2+4kx+3）的定义域为R，则实数 k 的取值范围是_。5（2008 江苏无锡模拟，5 分）给出下列四个命题：函数xay（0a且1a）与函数xaaylog（0a且1a）的定义域相同；函数3xy和xy3的值域相同；函数12121xy与xxxy2)21(2都是奇函数；函数2)1(xy与12xy在区间),0上都是增函数。其中正确命题的序号是：_。（把你认为正确的命题序号都填上）学习资料总结-名师归纳欢迎下载-欢迎下载名师归纳-第 6 页，共 6 页 -文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8文档编码:CR2K4R1U4K10 HA10F5W4Q5A10 ZA10R10U5G5W8

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