名校
1 . 已知函数
,若在定义域内存在
,使得
成立,则称
为函数
的局部对称点.
(1)若
,证明:函数
必有局部对称点;
(2)若函数
在区间
内有局部对称点,求实数
的取值范围;
(3)若函数
在
上有局部对称点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/744b07c137166e10db0b54001cb93a28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d20e107e902294bf57e7a584b66a6489.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6197c1aa468bec795a0fbcc097cdc792.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66bee5006333659a42d97f1aafd55ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa66623cf54b42d6d12be4c8edaa7071.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf10bf5b581a5826c48a1ba0b1d07529.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2020-03-01更新
|
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2卷引用:河南省郑州市八校2019-2020学年高一上学期期中联考数学试题
名校
解题方法
2 . 设函数
,
(
且
),若
.
(1)求函数
的定义域;
(2)判断
的奇偶性,并说明理由;
(3)求使
成立的
的集合.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6b52a845de8bcc6c6293985a317d27f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99f27a7ba8378e35ae0d766f090c5bf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf79a495595ec71447fcfa14b80e4dca.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
(3)求使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cc2395f479a7f620dc7a8168f87adef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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2020-03-01更新
|
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3卷引用:河南省郑州市八校2019-2020学年高一上学期期中联考数学试题
3 . 在如图所示的韦恩图中,
是非空集合,定义
表示阴影部分集合,若集合
,
,则
=____________ ;
=____________ ;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/422935d85056bc2fa6d4d50d034f62eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e9e460c144f7a2141d2df0308b125f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b40aace626f7615442c4cafe575588f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3858dcaffce6f63fc6ef6aa54fd2222d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e9e460c144f7a2141d2df0308b125f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7474df966fe3085468537375a15f48e6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/27/948223b4-8cc1-4020-ad70-456e1f9fc933.png?resizew=128)
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名校
4 . 记
表示
中的最大者,设函数
,若
,则实数
的取值范围是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a4461408813c1476a8a8073c83b8989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a14c388e1e2e5a2ff1ccf6caffbee0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df2efba684b6189e9768e21c53da23f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13169f688c1c3527de01a9cc1910a071.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2019-12-28更新
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226次组卷
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2卷引用:福建省龙岩市连城县第一中学2019-2020学年高一上学期第一次月考数学试题
名校
5 . 对于集合
,
,
,
,定义
.集合
中的元素个数记为
.规定:若集合
满足
,则称集合具
有性质
.
(1)已知集合
,
,写出
,
的值;
(2)已知集合
,其中
,证明:
有性质
;
(3)已知集合
,
有性质
,且
求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3a3f24673b6e954db3a8b229d8c4564.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5896fefe98d407d48fb709c4fb395363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9f41a0eb95a51bc64caca93cb3dc2cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/255a362a20eb766c90447c47894be6fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37fd01ea3d752dd68c7746c6c799b58e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc8279d9dd0b7750953cb9e2098b3b90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9821d668a92574d1bcb97aa93dc8108b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(1)已知集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6bf383bb9e68dde1d91355358d45d80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b82715ae3437616b568f9c45d4714781.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87b6ca4579d3b21f827a20b3e7b7ad58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/078cbd53c078b091c2bba4e55c98b2c9.png)
(2)已知集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9c0d49c56d6bcc3aeb47ec43fca8425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(3)已知集合
![](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/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c0e5a91adcedbb06079ac61fc82e84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c80d440b9478c09a6870403a8bd5cf38.png)
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解题方法
6 . 如果函数
的定义域为R,且存在实常数
,使得对于定义域内任意
,都有
成立,则称此函数
为“完美
函数”.
(1)判断函数
是否为“完美
函数”.若它是“完美
函数”,求出所有的
的取值的集合;若它不是,请说明理由.
(2)已知函数
是“完美
函数”,且
是偶函数.且当0
时,
.求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13d6a7c608eb0f2890472acb91803149.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f78d860493f5be44c5db1d70b16ba3c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc70c16151048d64bcb8e1e9b51e7d81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58662c77c9c991c980873224e050cdc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e34d0dcc6c8d3ec910b04cd20cba5be8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fda0bec3eb6c691fb27a016fd81dbc5b.png)
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7 . 对于正整数集合
(
,
),如果去掉其中任意一个元素
(
)之后,剩余的所有元素组成的集合都能分为两个交集为空集的集合,且这两个集合的所有元素之和相等,就称集合
为“和谐集”.
(1)判断集合
是否为“和谐集”,并说明理由;
(2)求证:集合
是“和谐集”;
(3)求证:若集合
是“和谐集”,则集合
中元素个数为奇数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a98a3d1f11a31e9ab1a3dde94c2d58d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ab46d077ba3d6e13fa1f6a5aaa0ce6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29577e558c82e3121c9ba2bb2fea875b.png)
(2)求证:集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cfb6c37f689c5a36be861291d1d488d.png)
(3)求证:若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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2019-11-15更新
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205次组卷
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2卷引用:上海市七宝中学2019-2020学年高一上学期期中数学试题
名校
8 . 对于集合
,定义函数
,对于两个集合
、
,定义集合
,用
表示有限集合
所含元素的个数,若
,
,则能使
取最小值的集合
的个数为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1e2cfa900e251ce107dc65f91e376c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4f2fe24792b22a6916520c1ea2c0533.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f60eacf71b95866a0ff3a5f81d1e62b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96adca1612848b337bb6a8daf4383f47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e74a5eb481325b47e22436f3ac8ff36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65b683ebd1325bf4ac83ecea80425aad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
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2卷引用:上海市七宝中学2019-2020学年高一上学期期中数学试题
名校
9 . 定义:若存在常数
,使得对定义域D内的任意两个不同的实数
,均有:
成立,则称
在D上满足利普希茨(Lipschitz)条件.
(1)试举出一个满足利普希茨(Lipschitz)条件的函数及常数
的值,并加以验证;
(2)若函数
在
上满足利普希茨(Lipschitz)条件,求常数
的最小值;
(3)现有函数
,请找出所有的一次函数
,使得下列条件同时成立:
①函数
满足利普希茨(Lipschitz)条件;
②方程
的根
也是方程
的根,且
;
③方程
在区间
上有且仅有一解.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de9bc59028761bee9de313ee6d5decc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(1)试举出一个满足利普希茨(Lipschitz)条件的函数及常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abfa1d9455db388617c1c3d0c5e98e7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bdfed8d6862125dc1fecfce0322a750.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)现有函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b923078510697d5f7f9ea392eb76dd9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
①函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
②方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f168b6811f1da5f09db1d9984ad8664f.png)
![](https://img.xkw.com/dksih/QBM/2019/11/12/2332484208558080/2333050301030400/STEM/b968951e37f142de95c41f25a4778494.png?resizew=9)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3047d4ab078dafc06c047bcbf0a6ffaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/918d58191d097e04f939343b6d57d07b.png)
③方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/298b861acdad2f218a882319c1a3280a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2e950e8a7181cb37bbddc6010fd87a2.png)
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10 . 设函数
的定义域为
,
,
,使得
成立,则称
为“美丽函数”.下列所给出的函数,其中是“美丽函数”的是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc1da2db85b44ae9ced8c09cd19593e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b1902ef70f2b5d826538d9e01809f01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30e88b679fa950ba6564946dc5828620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2019-10-30更新
|
1460次组卷
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7卷引用:山东省山东师范大学附中2019-2020学年高三上学期10月月考数学试题
山东省山东师范大学附中2019-2020学年高三上学期10月月考数学试题山东省菏泽第一中学老校区2019-2020学年高三12月月考数学试题2020届山东省临沂市郯城县高三上学期期末数学试题(已下线)专题4.4 指数函数、对数函数与幂函数(A卷基础篇)-2020-2021学年高一数学必修第二册同步单元AB卷(新教材人教B版)(已下线)6.3对数函数(1)-2021-2022学年高一数学链接教材精准变式练(苏教版2019必修第一册)(已下线)4.4 对数函数-2021-2022学年高一数学尖子生同步培优题典(人教A版2019必修第一册)苏教版(2019) 必修第一册 过关检测 第6章 第6.3节综合把关练