真题
1 . 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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