1 . 设
是函数
定义域内的一个子集,若存在
,使得
成立,则称
是
的一个“不动点”,也称
在区间
上存在不动点.
设函数
,
.
(1)若
,求函数
的不动点;
(2)若函数
在
上不存在不动点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28319174975bd87487e49585c65a79a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66f66a2b3d90f0d935d6c8ebaf675349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03e483e8a37a8e0e1fb327f99ad93ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dc44a740777dca624aa9d366dbc7b5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77538bd3aba1864f5eac30dae75b36d0.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724f1face977df2f57d4004e68d92b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
2 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8c6458979f861d9d422ab08f533921e.png)
.
(1)若
在
上为增函数,求实数
的取值范围;
(2)当
时,记
,求数列
的前
项和为
;
(3)当
时,且
,
,探求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8c6458979f861d9d422ab08f533921e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef075ca4f94a7afe1bc605bd0a6ee9ad.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8938db94f49dcbe0c383fba0241bb0da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e9222ffc26c0e6bfbf252ab5d8a520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35753e56bcf4452ea0ea8649b6fc9e8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe276c0522839b1d37086d92612aa7c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ffebb1edd03adae5b1b7535cf767847.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/514e1f85c6766dfcf633397a6f0208e8.png)
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名校
3 . 设
是定义在
上的函数,若存在
,使得
在
单调递增,在
上单调递减,则称
为
上的单峰函数,
为峰点,包含峰点的区间称为含峰区间,其含峰区间的长度为:
.
(1)判断下列函数中,哪些是“
上的单峰函数”?若是,指出峰点;若不是,说出原因;
;
(2)若函数
是
上的单峰函数,求实数
的取值范围;
(3)若函数
是区间
上的单峰函数,证明:对于任意的
,若
,则
为含峰区间;若
,则
为含峰区间;试问当
满足何种条件时,所确定的含峰区间的长度不大于0.6.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85b7e150af2052a1664cde963273d905.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9a801780561c48c27b05e3894de99a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eae40787b884e40c9fbff558491372d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13502d46b8563c54c09b29b20b3006a4.png)
(1)判断下列函数中,哪些是“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/304226ca50149b49702928e44d565964.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c29d3981fe4fc667bfc4b9ab72a0f938.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d99175f13f12333b9bf574b79cf38e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9210e75c35fb455d0446eb7ddba7d79c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/304226ca50149b49702928e44d565964.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa1825e7e125bba03a5617d0ebe2830.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ce40da2cbd52723210bbfa98a7f81b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14283f108568721e6d9ec8d42036be33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25ba30f1aa5e75750c67b142fc1d7837.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f2a570f0086433e604736679f7192c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
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名校
4 . 设定义在
上的函数
满足:对任意的
,当
时,都有
.
(1)若
,求实数
的取值范围;
(2)若
为周期函数,证明:
是常值函数;
(3)若
在
上满足:
,
,
,
①记
(
),求数列
的通项公式;② 求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fd423a80d5b6fea8753fa1813cfbcc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25ba30f1aa5e75750c67b142fc1d7837.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e44a0f74224978afe9b6cfe323228d29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/304226ca50149b49702928e44d565964.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/104375baf5cef5eb92cfc7cf13b80193.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2493344c3e6aa5e038c98ee6d60bb62d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac4378305ae8e20c68036c4e079dd59d.png)
①记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88005ca8be513a9dcebdbb2ecbd6d76b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fde47a508fb6fe6b617f0062caa50676.png)
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5 . 已知函数
.
(1)当
时,判断
的单调性;
(2)若
在
上为单调增函数,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/889bc668d3fdfd9d8aa39a0072fb9666.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82f6f7ea32b59cd8beeb2d6bb74632bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
6 . 已知函数
.
(1)当
时,函数
在区间
上的最大值为
,试求实数
的取值范围;
(2)当
时,若不等式
对任意
)恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b15d80383c5d80acb9186902730ae986.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dfe1f31f4a31f7adfe6a07757543ceb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d4f2f6133b09cb067e056ad0bd9919.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3f81f2a0196b06fc56a7e8a6463d179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f039953f09677969db031e357ec8a208.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a04be122c33d40ebb4408aa697dc3e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b57deea397cb002060497dc08484a382.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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2016-12-04更新
|
590次组卷
|
3卷引用:2015届浙江省嘉兴市高三下学期教学测试二理科数学试卷
真题
7 . 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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12-13高三上·上海闵行·期末
8 . 记函数
在区间D上的最大值与最小值分别为
与
.设函数
,
.
.
(1)若函数
在
上单调递减,求
的取值范围;
(2)若
.令
.
记
.试写出
的表达式,并求
;
(3)令
(其中I为
的定义域).若I恰好为
,求b的取值范围,并求
.
![](https://img.xkw.com/dksih/QBM/2012/1/11/1570683802361856/1570683807817728/STEM/9582e889d13842e4a2b52304ad335f7b.png?resizew=36)
![](https://img.xkw.com/dksih/QBM/2012/1/11/1570683802361856/1570683807817728/STEM/53f354149439482da1d81e60a86a9f15.png?resizew=124)
![](https://img.xkw.com/dksih/QBM/2012/1/11/1570683802361856/1570683807817728/STEM/60487e13589d4084be1cb28b17b5e125.png?resizew=120)
![](https://img.xkw.com/dksih/QBM/2012/1/11/1570683802361856/1570683807817728/STEM/6f2afa29c68d46ab88921ed94baa0081.png?resizew=164)
![](https://img.xkw.com/dksih/QBM/2012/1/11/1570683802361856/1570683807817728/STEM/c2183a799b544492b6776971b869a0c5.png?resizew=58)
![](https://img.xkw.com/dksih/QBM/2012/1/11/1570683802361856/1570683807817728/STEM/49eeef9ae20e455fb375f0dbbd9cf19a.png?resizew=167)
(1)若函数
![](https://img.xkw.com/dksih/QBM/2012/1/11/1570683802361856/1570683807817728/STEM/76ac75f86cd74dcf9d8acac87bc12c95.png?resizew=35)
![](https://img.xkw.com/dksih/QBM/2012/1/11/1570683802361856/1570683807817728/STEM/365e5307876349a09d5103890ca50a5a.png?resizew=32)
![](https://img.xkw.com/dksih/QBM/2012/1/11/1570683802361856/1570683807817728/STEM/be336b753bd144ea8f785d43a97a9ad3.png?resizew=13)
(2)若
![](https://img.xkw.com/dksih/QBM/2012/1/11/1570683802361856/1570683807817728/STEM/001344f6940a4163acd9f77fdd9d21cf.png?resizew=40)
![](https://img.xkw.com/dksih/QBM/2012/1/11/1570683802361856/1570683807817728/STEM/46c1243c1ae34ce9b43742c58f311d92.png?resizew=324)
记
![](https://img.xkw.com/dksih/QBM/2012/1/11/1570683802361856/1570683807817728/STEM/57f9462183dc4730be1b0bfbcdaf9bb3.png?resizew=161)
![](https://img.xkw.com/dksih/QBM/2012/1/11/1570683802361856/1570683807817728/STEM/59860422c5cf40d5be610ccd63219d14.png?resizew=33)
![](https://img.xkw.com/dksih/QBM/2012/1/11/1570683802361856/1570683807817728/STEM/9c6ceeb3217b452aac763d88c9ebd64c.png?resizew=128)
(3)令
![](https://img.xkw.com/dksih/QBM/2012/1/11/1570683802361856/1570683807817728/STEM/fe89ba8a284143018aca801659c743f1.png?resizew=332)
![](https://img.xkw.com/dksih/QBM/2012/1/11/1570683802361856/1570683807817728/STEM/eff96ecb4c384b07b7222437d08f0b68.png?resizew=55)
![](https://img.xkw.com/dksih/QBM/2012/1/11/1570683802361856/1570683807817728/STEM/eb3a591ebfb449fd9137aee39fe96be5.png?resizew=36)
![](https://img.xkw.com/dksih/QBM/2012/1/11/1570683802361856/1570683807817728/STEM/ae029b52880b4719b66451df4d7d0dc2.png?resizew=105)
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