抽象函數(shù)的單調(diào)性

1、1抽象函數(shù)的單調(diào)性抽象函數(shù)的單調(diào)性抽象函數(shù)的含義：沒有解析式的函數(shù)，在考試中抽象函數(shù)始終作為一大難點(diǎn)出現(xiàn)在考生面前。抽象函數(shù)的含義：沒有解析式的函數(shù)，在考試中抽象函數(shù)始終作為一大難點(diǎn)出現(xiàn)在考生面前。思路：添項(xiàng)法。思路：添項(xiàng)法。類型：一次函數(shù)型，冪函數(shù)型，指數(shù)函數(shù)型，對(duì)數(shù)函數(shù)型。類型：一次函數(shù)型，冪函數(shù)型，指數(shù)函數(shù)型，對(duì)數(shù)函數(shù)型。一類：一次函數(shù)型一類：一次函數(shù)型函數(shù)滿足：函數(shù)滿足：或()()()fabfafbk????()()()fabf

2、afbk????例1、對(duì)任意都有：，當(dāng)，判斷在R上的單調(diào)性。()fxxyR?()()()fxyfxfy???0()0xfx??時(shí)()fx????????????上是增函數(shù)在解：RxfxfxfxxfxxxxxxfxfxfxxfxfxxxfxfxfxxRxx)(00)(0)()()()(212121212122212221212121????????????????????????例2、f(x)對(duì)任意實(shí)數(shù)x與y都有當(dāng)x0時(shí)f(x)2()()

3、()2fxfyfxy????（1）求證:f(x)在R上是增函數(shù)；（2）若f(1)=52解不等式f(2a3)1。2、若非零函數(shù)對(duì)任意實(shí)數(shù)均有，且當(dāng)時(shí)，；)(xfba()()()fabfafb???0?x1)(?xf（1）求證：；（2）求證：為減函數(shù)（3）當(dāng)時(shí)，解不等式()0fx?)(xf161)4(?f；41)5()3(2????xfxf四類：冪函數(shù)型四類：冪函數(shù)型函數(shù)滿足：函數(shù)滿足：或()()()fabfafb?AA()()()afaf