真题
1 . 已知函数
a为常数且a>0.
(1)证明:函数f(x)的图像关于直线x=
对称;
(2)若x0满足f(f(x0))= x0,但f(x0)≠x0,则x0称为函数f(x)的二阶周期点,如果f(x)有两个二阶周期点x1,x2,试确定a的取值范围;
(3)对于(2)中的x1,x2,和a,设x3为函数f(f(x))的最大值点,A(x1,f(f(x1))),B(x2,f(f(x2))),C(x3,0),记△ABC的面积为S(a),讨论S(a)的单调性.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/532b8d832cbb3f4f40cbc9a3de106529.png)
(1)证明:函数f(x)的图像关于直线x=
![](https://img.xkw.com/dksih/QBM/2014/5/22/1578311980425216/1578311980924928/STEM/15505c2a65764958a0b2357a299427f8.png)
(2)若x0满足f(f(x0))= x0,但f(x0)≠x0,则x0称为函数f(x)的二阶周期点,如果f(x)有两个二阶周期点x1,x2,试确定a的取值范围;
(3)对于(2)中的x1,x2,和a,设x3为函数f(f(x))的最大值点,A(x1,f(f(x1))),B(x2,f(f(x2))),C(x3,0),记△ABC的面积为S(a),讨论S(a)的单调性.
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真题
2 . 若函数h(x)满足
(1)h(0)=1,h(1)=0;
(2)对任意
,有h(h(a))=a;
(3)在(0,1)上单调递减.则称h(x)为补函数.已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aff1b30ab638d5332fa2419fc943e57d.png)
(1)判函数h(x)是否为补函数,并证明你的结论;
(2)若存在
,使得h(m)=m,若m是函数h(x)的中介元,记
时h(x)的中介元为xn,且
,若对任意的
,都有Sn<
,求
的取值范围;
(3)当
=0,
时,函数y= h(x)的图像总在直线y=1-x的上方,求p的取值范围.
(1)h(0)=1,h(1)=0;
(2)对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aad79505d991ab451d8299b8e3ea4f2.png)
(3)在(0,1)上单调递减.则称h(x)为补函数.已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aff1b30ab638d5332fa2419fc943e57d.png)
(1)判函数h(x)是否为补函数,并证明你的结论;
(2)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cadeb033934e231e35c378131be5abd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6505f7fb491d11d65e3c196fa8b6e58e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a12f0ec811fa93b4b191a2fb7e3244f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29d5ec9ad92f37e64eccce922ab1b14e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ac2dec993e1dcd5d8a848298ba0080.png)
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真题
3 . 已知函数
,
.
(1)当
时,求
的单调区间;
(2)对任意正数
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc312f3f7ee4997ab1f66bd68af55b6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18852c5e9474249613b566e8ea59734f.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e15cbd7c42d7b15d7ba8d2b28ab8df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)对任意正数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad0cb3a21735c5a762c67614e3ce9e0f.png)
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2010-03-31更新
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1611次组卷
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2卷引用:2008年普通高等学校招生全国统一考试理科数学(江西卷)