1 . 集合
由有限个实数组成,定义集合
的离距
如下:实数轴上,集合
中的每个实数
对应一个点
,实数
对应的点
与所有这些点
的距离的算术平均数记为
,称函数
的最小值为集合
的离距,记为
.例如,集合
的离距是0,集合
的离距是2.
(1)分别求出集合
的离距;
(2)求数集
的离距;
(3)已知非空数集
满足
,试写出一个关于
的大小关系的等式或不等式,并给出证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fdb777c90f9cabba8d4ed34c16f4acb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e51c8010a4568d7d44f261973dea420.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fdb777c90f9cabba8d4ed34c16f4acb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39412925212a989c503e891db840609d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21c6fed9c3cf2c00ba1823c3f0a05615.png)
(1)分别求出集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7384a3e8b9a7ffb00bb124ba97b7c992.png)
(2)求数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22accc2928d3370f48a84cc4703a4b07.png)
(3)已知非空数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b21e6c4bb62b14f8e70d8f8b1ac911bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3598ab9c4ac9a9496c5f34b9b5fda3cf.png)
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2 . 设
,如果函数
:
的值域也是
,则称之为一个泛函数,并定义其迭代函数列
:
,
.
(1)请用列表法补全如下函数列;
(2)求证:对任意一个
,存在正整数
(
是与
有关的一个数),使得
;
(3)类比排序不等式:
,
,把
中的10个元素按顺序排成一列记为
,使得10项数列
:
,
,
,…,
的所有项和
最小,并计算出最小值
及此时对应的
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a0367345901c5a716dca179385158c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84315a088ff3d8b91be22d3b3fcd92ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f99442281052744a6b74b32e0fc2536f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66a88cbaed58dcf9671ba9240359b9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89b2c1a76a73797e9d5699f6c9929a50.png)
(1)请用列表法补全如下函数列;
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
2 | 1 | 7 | 5 | 3 | 4 | 9 | 10 | |||
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/002bda38860f9cbc17dd7b6a03cfecf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24d5926ad4ccd91c0ec7ff14018de8b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5328785361a76b5e8f75b034a07c5e35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b526c87ad796e8cd189f88c33c8d8fd.png)
(3)类比排序不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a46e678bf9d2df5ad4c782b3dc22f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0109ae0739494164db5b7edae7bfb2e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd643dcc6985a78b5dfe3127610e920e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eee7088c883282e2f7d95a1856902fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87139b2d092ad22a082bd2a9fa31901d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4aac3646575e397de3dee4ed5d1060b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38f27bc508f582e07211ee24d01bc551.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e77ac9dd1c3046137614c0f62e55190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd643dcc6985a78b5dfe3127610e920e.png)
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解题方法
3 . 已知集合A为数集,定义
.若
,定义:
.
(1)已知集合
,直接写出
,
及
的值;
(2)已知集合
,
,
,求
,
的值;
(3)若
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de527cec4114ceaa27f3d5b7f8e5fee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05d29488289a3db7cb65894175be30f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1d7e2e5ccdad8b47fc0806607620820.png)
(1)已知集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45162ca60403d0d044c73a51dee654aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f03e23c5f50122bd65c621c69f301f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6736b4cf3b5d77b25fff47f5325ab8cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/097a5083399b56ae6d34a5482ae6d23b.png)
(2)已知集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ca717c6a55e786238e64f7ebd69b9b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c105e7649e4eff5001fd62952855ec1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d3e5d65f77e868e505e905f0d909187.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3bcb4828b16c8e845492f1a53ddd9a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5a6e825795c828f8281e93607d0e1b1.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f03916a8247604a610e1a93424cb1ce2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24307d79a1906db6176f80389b5c5004.png)
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名校
4 . 设集合
为
元数集,若
的2个非空子集
满足:
,则称
为
的一个二阶划分.记
中所有元素之和为
中所有元素之和为
.
(1)若
,求
的一个二阶划分,使得
;
(2)若
.求证:不存在
的二阶划分
满足
;
(3)若
为
的一个二阶划分,满足:①若
,则
;②若
,则
.记
为符合条件的
的个数,求
的解析式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e05aa7f57c4914f5248f44b09def2c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20106a23af649dffb3571082e5a9cfdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09f78031a7d18c8f8ddf04bffd1871.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ca717c6a55e786238e64f7ebd69b9b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43de850d8546d0933b37846a84f90bc5.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f76be59eef5f019579f1f5b936b98b72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41212f1139ba1b062d7f40ec7120a9bf.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f12f339b0f68f0739fdfcb39ec4f7eb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23af61cd402b3789af2401bde9cbefe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10732f3fb10019cb15c3c46d118f7da5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3eb5935678e432e6f1f3180bfdb3175.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29f19c9afadbf80e1e6b5b3a673e6270.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fcec7af3520884b173b29bda6c657a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fcec7af3520884b173b29bda6c657a.png)
您最近一年使用:0次
2023-07-17更新
|
551次组卷
|
5卷引用:北京市顺义区2022-2023学年高一下学期期末质量监测数学试题
北京市顺义区2022-2023学年高一下学期期末质量监测数学试题重庆市南开中学校2023-2024学年高一上学期开学考试数学试题(已下线)难关必刷01集合的综合问题(3种题型40题专项训练)-【满分全攻略】(人教A版2019必修第一册)(已下线)第三章 函数的概念与性质-【优化数学】单元测试能力卷(人教A版2019)(已下线)专题03 函数的概念与性质3-2024年高一数学寒假作业单元合订本
5 . 已知集合
是集合
的子集,对于
,定义
.任取
的两个不同子集
,
,对任意
.
(1)判断
是否正确?并说明理由;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22d39a39a70dacd0402f6fdd59a0e879.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc718cf6749da06b2dd90e9b2751854.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e1171081d25910d6bb0bf9d32e82e33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22d39a39a70dacd0402f6fdd59a0e879.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc718cf6749da06b2dd90e9b2751854.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51ac3d72ad811d426884f100f32aa0a2.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4090eff6726fa4e3a32655b3fba41abe.png)
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6 . 已知函数
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/882cd70e-41a3-4411-b912-ba36adc0e946.png?resizew=208)
(1)求
;
(2)若
,求
的值;
(3)若函数
的图象与直线
有三个交点,请画出函数
的图象并写出实数
的取值范围(不需要证明).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1f3bf39c3a0cd87de6adfa5a202d396.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/882cd70e-41a3-4411-b912-ba36adc0e946.png?resizew=208)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/754386f1d84e582d52d8219080a81528.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32e9089e21e10f127e970d8e42e55244.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff4d12362d4b8dd25813953e1c5a94b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
名校
7 . 设函数
,
,且对所有的实数
,等式
都成立,其
、
、
、
、
、
、
、
,
、
.
(1)如果函数
,
,求实数
的值;
(2)设函数
,直接写出满足
的两个函数
;
(3)如果方程
无实数解,求证:方程
无实解.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d1e8682621b95ad887ea391340a73ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c3a9184d813c0ff9c6a719ec430463c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2154c82b84741b9afc407845e546d80f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35f7dcce39f3d4dc6b7faf84dc1d0a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f74901036e0163ee8f9e88e1d952aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b715e7842b95f654f16056a7c7f2abe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6db583bbab30ac1017e37098c0cce2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac69e6db1df13ed64756b4f391ae9fac.png)
(1)如果函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f31e7b314a440efd192a160ec8f3290c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45ae5bf586180be873beb79280319055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448ebc0073967335c4f07ae0f997b72a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2154c82b84741b9afc407845e546d80f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
(3)如果方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f88653ab06d6f3fa74fff528b0255c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdde71f9c85a707bbfdcbec0a0a24a78.png)
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