高考數(shù)學(xué)函數(shù)題庫(kù)

1、函數(shù)題庫(kù)函數(shù)題庫(kù)11.（2010全國(guó)卷Ⅰ理）函數(shù)()fx的定義域?yàn)镽，若(1)fx?與(1)fx?都是奇函數(shù)，則()A.()fx是偶函數(shù)B.()fx是奇函數(shù)C.()(2)fxfx??D.(3)fx?是奇函數(shù)答案D解析?(1)fx?與(1)fx?都是奇函數(shù)，(1)(1)(1)(1)fxfxfxfx???????????，?函數(shù)()fx關(guān)于點(diǎn)(10)，及點(diǎn)(10)?對(duì)稱，函數(shù)()fx是周期2[1(1)]4T????的周期函數(shù).(14)(14

2、)fxfx????????，(3)(3)fxfx?????，即(3)fx?是奇函數(shù)。故選D2.(2010浙江理）對(duì)于正實(shí)數(shù)?，記M?為滿足下述條件的函數(shù)()fx構(gòu)成的集合：12xx??R且21xx?，有212121()()()()xxfxfxxx????????下列結(jié)論中正確的是()A若1()fxM??，2()gxM??，則12()()fxgxM?????B若1()fxM??，2()gxM??，且()0gx?，則12()()fxMgx?

3、??C若1()fxM??，2()gxM??，則12()()fxgxM?????D若1()fxM??，2()gxM??，且12???，則12()()fxgxM?????答案C解析對(duì)于212121()()()()xxfxfxxx????????，即有2121()()fxfxxx???????，令2121()()fxfxkxx???，有k?????，不妨設(shè)1()fxM??，2()gxM??，即有11fk?????22gk?????，因此有12

4、12fgkk??????????，因此有12()()fxgxM?????3.（2010浙江文）若函數(shù)2()()afxxax???R，則下列結(jié)論正確的是（）A.a??R，()fx在(0)??上是增函數(shù)函數(shù)題庫(kù)函數(shù)題庫(kù)3【命題立意】:本題考查歸納推理以及函數(shù)的周期性和對(duì)數(shù)的運(yùn)算.6.(2009山東卷文)函數(shù)xxxxeeyee?????的圖像大致為().答案A.解析函數(shù)有意義需使0xxee???其定義域?yàn)??0|?xx排除CD又因?yàn)?2212

5、111xxxxxxxeeeyeeee???????????所以當(dāng)0x?時(shí)函數(shù)為減函數(shù)故選A.【命題立意】:本題考查了函數(shù)的圖象以及函數(shù)的定義域、值域、單調(diào)性等性質(zhì).本題的難點(diǎn)在于給出的函數(shù)比較復(fù)雜需要對(duì)其先變形再在定義域內(nèi)對(duì)其進(jìn)行考察其余的性質(zhì).7.(2009山東卷文)定義在R上的函數(shù)f(x)滿足f(x)=?????????0)2()1(0)4(log2xxfxfxx，則f（3）的值為()A.1B.2C.1D.2答案B解析由已知得2(1

6、)log5f??2(0)log42f??2(1)(0)(1)2log5fff?????2(2)(1)(0)log5fff????22(3)(2)(1)log5(2log5)2fff????????故選B.【命題立意】:本題考查對(duì)數(shù)函數(shù)的運(yùn)算以及推理過(guò)程.8.(2009山東卷文)已知定義在R上的奇函數(shù))(xf，滿足(4)()fxfx???且在區(qū)間[02]上是增函數(shù)則().A.(25)(11)(80)fff???B.(80)(11)(25)