名校
1 . 设
,
,在集合
的所有元素个数为2的子集中,把每个子集的较大元素相加,和记为
,较小元素之和记为
.
(1)当
时,求
,
的值;
(2)求证:为任意的
,
,
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1534b035eca39010118a83486de8904.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb8c29b297e3ec337c3139c2a1ebed1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/330a768883271ebe0b692f6c226867a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6862dd3c43647ce7d7935a7d205b54d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)求证:为任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1534b035eca39010118a83486de8904.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb8c29b297e3ec337c3139c2a1ebed1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f563f31a226905e5b38ca81078a1af35.png)
您最近一年使用:0次
2018-06-23更新
|
1103次组卷
|
2卷引用:【全国百强校】江苏省泰州中学2017-2018学年高二6月月考数学(理)试题
名校
2 . 记函数
的定义域为D. 如果存在实数
、
使得
对任意满
足
且
的x恒成立,则称
为
函数.
(1)设函数
,试判断
是否为
函数,并说明理由;
(2)设函数
,其中常数
,证明:
是
函数;
(3)若
是定义在
上的
函数,且函数
的图象关于直线
(m为常数)对称,试判断
是否为周期函数?并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8d8d7f3bab030b7301b1f8ffde25235.png)
足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2d73ff48d69b4a7d1fb3a19f1cdfb1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b14436281d0445ba9a5321cbb34d3ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4370226c16822cf9bbc390444c581bf.png)
(1)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d79f4673f430b3e9940b768323871cb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4370226c16822cf9bbc390444c581bf.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84cba018ab7f525ca0e1d21179d7e0a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/823ab696d27d40920c39b8c910789380.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4370226c16822cf9bbc390444c581bf.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4370226c16822cf9bbc390444c581bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36d71f015144ffaf1faec94a259b4a06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
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2018-04-12更新
|
744次组卷
|
2卷引用:上海市杨浦区2018届高三下学期质量调研(二模)数学试题
3 . 已知函数
.
(1)若
恒成立,试确定实数
的取值范围;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ebc0939e9a3f9951add30e16e101170.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dc9ede2e55724383dd1093fc7fcdb59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/653d9110904f73ce48165b06b7c29a50.png)
您最近一年使用:0次
名校
4 . 函数f(x)的定义域D={x|x≠0},且满足对于任意x1,x2∈D.有f(x1·x2)=f(x1)+f(x2).
(1)求f(1)的值;
(2)判断f(x)的奇偶性并证明;
(3)如果f(4)=1,f(3x+1)+f(2x-6)≤3,且f(x)在(0,+∞)上是增函数,求x的取值范围.
(1)求f(1)的值;
(2)判断f(x)的奇偶性并证明;
(3)如果f(4)=1,f(3x+1)+f(2x-6)≤3,且f(x)在(0,+∞)上是增函数,求x的取值范围.
您最近一年使用:0次
2018-09-08更新
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1643次组卷
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8卷引用:2016-2017学年辽宁省盘锦市辽河油田第二高中高一10月考数学试卷
5 . 数列
:
满足:
.记
的前
项和为
,并规定
.定义集合
,
,
.
(Ⅰ)对数列
:
,
,
,
,
,求集合
;
(Ⅱ)若集合
,
,证明:
;
(Ⅲ)给定正整数
.对所有满足
的数列
,求集合
的元素个数的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd0c872bad2e600189aaa363bace8864.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4746aa748f575e5d289250c97ab79865.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d0a9523f2084cf17b8656c11ab1d95e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5bf3787395e2a714652e29836339a1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d341538a1a88276483c192ccce5753.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa5ac393fa1d6e785898385c6db24557.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51cf1c7fe656fb3a27d51ade754f636b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4f182073bbd9d36fcdbfbde808107a7.png)
(Ⅰ)对数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5002f030017f6f0b34a61b2e15c5a9cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c75d883636eb033325f4ac5f1d4235d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29ee5940db3eca3be22205d12bae26e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/217bd7beedf538080da855720e15fe1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52dbd64028ab37a28942a961993ad21d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a87796ee30e6c5d5e6b6285b32abe10c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21aba556a5b9e2a76eb03ed6c0ff475d.png)
(Ⅱ)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6a3f0e61a59077c1f34344c4a24a155.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cf90e68904b8191961496a629e74888.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c6838bc2b98c171302b2b813445535c.png)
(Ⅲ)给定正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19fd1ffc360f0e882f423d7f8cb2cb15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a78b3c84e7818ed70018eea40c72665.png)
您最近一年使用:0次
2018-09-01更新
|
451次组卷
|
5卷引用:北京市城六区2018届高三一模理科数学解答题分类汇编之压轴创新题
北京市城六区2018届高三一模理科数学解答题分类汇编之压轴创新题(已下线)2019年一轮复习讲练测【新课标版理】第一章测试卷2020届北京市东城区高三一模线上统练数学(二)试题广西桂林市临桂区第三中学2024届高三下学期4月月考数学试卷(已下线)第一章 集合与常用逻辑用语、不等式(测试)
名校
6 . 已知函数
且满足条件:①
;②
.
(1)求
的表达式;
(2)当
时,证明:
;
(3)若函数
,讨论
在
上的零点个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bd84c3eca164b295975ca9140f38380.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/834ef0cebcd0dff24529d3b4992f0c0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ca809269dc3e07476d0ff0c15fd177d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/725173c99b6fbb958cdab101569985dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44ce0672fd522ab1f84edf7c50f04b67.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a536cfec322a455e160e82bd82d69525.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e534d9cfe96e9921be8e3a95d56fb73.png)
您最近一年使用:0次
名校
7 . 已知集合
,其中
,
,
.
表示
中所有不同值的个数.
(
)设集合
,
,分别求
和
.
(
)若集合
,求证:
.
(
)
是否存在最小值?若存在,求出这个最小值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb9e56ab45ddf991ae24983027e04b08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d0c23fa72e4bbbdef69895aef768c03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ef835c9ad2636a9662fb6c99e3abc78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9153fb853cd99beec9e600a4eaf73fe8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/403eef43448ff6ba342ed0ad5c4b5978.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28542a0186cd714deaa181efadff87cd.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef27cd09f4ecc055fd7e72b3b368e5df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/746a3b7cb3c7ac223c8aa0d4b93ae093.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3851739b3d70143beaca9621b265871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce6942492388c0805d27db3a9b8a345.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/972fd1bc03c253c043535a8425cfabab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5675fc66a66c7cd74516987fa758984.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/403eef43448ff6ba342ed0ad5c4b5978.png)
您最近一年使用:0次
2018-03-30更新
|
574次组卷
|
4卷引用:北京市东城东直门中学2017-2018学年高三上期中数学试题
北京市东城东直门中学2017-2018学年高三上期中数学试题北京市海淀区教师进修附属实验学校2019~2020学年高一第二学期期中考试数学试题(已下线)数学-6月大数据精选模拟卷05(北京卷)(满分冲刺篇)北京市宣武外国语实验学校2021届高三上学期期中考试数学试题
8 . 已知集合
…,
…,
,对于
…,
,B=(
…,
,定义A与B的差为
…
,A与B之间的距离为
.
(Ⅰ)若
,求
;
(Ⅱ)证明:对任意
,有
(i)
,且
;
(ii)
三个数中至少有一个是偶数;
(Ⅲ)对于
…
…
,再定义一种A与B之间的运算,并写出两条该运算满足的性质(不需证明).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c021903301e63c85bdac9261a5d594a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09c282f2f68d146875d66a22e32156d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb8dfd907730c129405573e9cf70768a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9355ed4ae10378e1ffa36a84967bf678.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11e3810cf1eca832ef7487d354e474d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c5ae42941d2202aa97872f86d5a2edc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8881be24c60a78047026994651d354f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d3e87eee4512c4c092f391b2651e4c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fb1834928d33b241ae00de686dc7bef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/badd0969b43deabb1e8f3fcca73ce1c5.png)
(Ⅰ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/084e6a917203c6c560bad1791a4643a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3c11e3798218ef9e0c49b1362403f4f.png)
(Ⅱ)证明:对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81345ca73b711411e665820b5672913d.png)
(i)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42a0663324985d2901305e58b066e763.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8513f18376e4e456b939d0f1cdb6e602.png)
(ii)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8430e22ff50167e4de289cc378c0bc3f.png)
(Ⅲ)对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1faceea22e6964ad3f57082c04c6121c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f398af70e8dc7fa5c732ca48820a7638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f219f94d64f1ef5fbf3e052993cd37eb.png)
您最近一年使用:0次
2018-06-13更新
|
674次组卷
|
2卷引用:【全国百强校】北京师范大学附属中学2017-2018学年下学期高一年级期中考试数学试题
名校
解题方法
9 . 一般地,我们把函数
称为多项式函数,其中系数
,
,…,
.设
,
为两个多项式函数,且对所有的实数
等式
恒成立.
(1)若
,
.
①求
的表达式;
②解不等式
.
(2)若方程
无实数根,证明方程
也无实数解.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5bf5ba3261da10ef4c78b5d611aaf60.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/96a5d7258973bf6c6afab73fcc1e8263.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34c3e5078eacd04040a3b843f2f8a894.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df4ab5ed446cb4d85ee8f9e93e0985e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb4935611969e644511329f6b0dbbf3b.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
②解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca77cbddad9b9b82ee918612de679f27.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f8bfb563f79688d136e0cb958b5153c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ed16a1c5b976b543af7d418a9e4905.png)
您最近一年使用:0次
2017-10-31更新
|
455次组卷
|
3卷引用:北京西城35中2016-2017学年高一上学期期中数学试题
10 . 已知函数
.
(1)判断函数
的奇偶性;
(2)对任意两个实数
,求证:当
时,
;
(3)对任何实数
,
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/956f5a1abb489955154b94cd109ecc0b.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)对任意两个实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7ec808ad60dbf016632ec816eaca1df.png)
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