解题方法
1 . 已知函数
是R上的偶函数,
是R上的奇函数,且
,求证:
是周期函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/388141c33eea9e11831be8c061283570.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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名校
2 . 设
,已知由自然数组成的集合
,集合
,
,…,
是
的互不相同的非空子集,定义
数表:
,其中
,设
,令
是
,
,…,
中的最大值.
(1)若
,
,且
,求
,
,
及
;
(2)若
,集合
,
,…,
中的元素个数均相同,若
,求
的最小值;
(3)若
,
,集合
,
,…,
中的元素个数均为3,且
,求证:
的最小值为3.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c61a450b5c1c412aca3294e9eb4e9874.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1221e342a03bd2806e0993c996827ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1752474698cd5466dd180df0a00ba9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0abc7b7ef8b7a91099ca63ea1aaf7cfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e6571a9572dc91c90da43a5390f69d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33b2c4a940739711008be65a1fad4146.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6ac1a105450fef08656cf15a10e7fe7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87b87cd94fef6e528d0913bb1b7b53de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b47771d50cf28b8f528afda24720eb8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c52ce6355f8b297a89f20f2e7f48041d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5beea8e2b24bdc221f6c16e46efdf665.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8a3cc8c48bf54ec8252e5dce6867754.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/862353b1d19b5e38a60c4ceeb2b01913.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed4e4ea995fa993d6a55c2e523fa8ae1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87b87cd94fef6e528d0913bb1b7b53de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/568bcf1a46049068d2dc34af9d0b991c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1752474698cd5466dd180df0a00ba9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bad28732b9ef03fa2a2fcabe344c27b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6caddd958ae597c7a1f8f6a9ee2a3200.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff794a4d07295ba8002c36f9c6054f86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/194592cb77de8a597d5d64e1c85c3249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ece66a27e197695e0f02e1a0afa4a0d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87b87cd94fef6e528d0913bb1b7b53de.png)
您最近一年使用:0次
2023-07-10更新
|
680次组卷
|
4卷引用:北京市朝阳区2022-2023学年高一下学期期末质量检测数学试题
北京市朝阳区2022-2023学年高一下学期期末质量检测数学试题北京市陈经纶中学2023-2024学年高二上学期开学检测数学试题(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)高一上学期期末考试解答题压轴题50题专练-举一反三系列
名校
解题方法
3 . 已知函数
是奇函数.
(1)求b的值;
(2)证明
在R上为减函数;
(3)若不等式
成立,求实数t的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0809f2d1e9db2cab02ec073988614659.png)
(1)求b的值;
(2)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29321159c06e47055b2fc30cc1c5e8d8.png)
您最近一年使用:0次
2023-04-17更新
|
934次组卷
|
7卷引用:重庆市2022-2023学年高一下学期6月月考数学试题
重庆市2022-2023学年高一下学期6月月考数学试题(已下线)专题10 指数及指数函数压轴题-【常考压轴题】(已下线)高一数学上学期期中考试模拟卷-【巅峰课堂】热点题型归纳与培优练江苏省镇江市扬中市第二高级中学2023-2024学年高一上学期期中考试数学试卷广东省东莞市东莞外国语学校2023-2024学年高一上学期第二次段考(11月)数学试题福建省泉州市第九中学2021-2022学年高一上学期期中考试数学试题江苏省连云港市海滨中学2023-2024学年高一上学期第二次学情检测(12月)数学试题
4 . 已知函数
.
(1)判断
的奇偶性;
(2)若
,判断
在
的单调性,并用定义法证明;
(3)若
,
,判断函数
的零点个数,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaf6edebbf204ca0e7462d7ece59fca1.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7d013331d969749c306909529a88a49.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ada9b792b1555668175c590447b02fb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
您最近一年使用:0次
2023-05-25更新
|
921次组卷
|
3卷引用:专题03E函数解答题
名校
解题方法
5 . 已知
是非空数集,如果对任意
,都有
,则称
是封闭集.
(1)判断集合
是否为封闭集,并说明理由;
(2)判断以下两个命题的真假,并说明理由;
命题
:若非空集合
是封闭集,则
也是封闭集;
命题
:若非空集合
是封闭集,且
,则
也是封闭集;
(3)若非空集合
是封闭集合,且
为全体实数集,求证:
不是封闭集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e13a814f8e081078dcf3788177affcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6493575a2d595bebd8e813c3d79fb8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8bb6359407782248c8be98288b1791e.png)
(2)判断以下两个命题的真假,并说明理由;
命题
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2646f41226f24960a6186dc7860ef45.png)
命题
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a8543bb9be52b25cf5be0a39110c9e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b76d26b78e63683dfacf10d3da6d74d.png)
(3)若非空集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ba5283c1fa3bf7896113cd79e9c31d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49c6009ab1bad0e053bc7e11b868cac6.png)
您最近一年使用:0次
2023-01-06更新
|
790次组卷
|
8卷引用:北京市顺义区2022-2023学年高一上学期期末质量监测数学试题
北京市顺义区2022-2023学年高一上学期期末质量监测数学试题第一章 预备知识 测试卷-2022-2023学年高一上学期数学北师大版(2019)必修第一册(已下线)1.1集合的概念(分层作业)-【上好课】(已下线)1.3 集合的基本运算(精练)-《一隅三反》(已下线)专题02 高一上期中真题精选-期中考点大串讲(人教A版2019必修第一册)(已下线)专题1 集合新定义题(九省联考第19题模式)练(已下线)周测1 集合与常用逻辑用语 一轮周测卷(提升卷)湖南省岳阳市2022-2023学年高一下学期期中数学试题
名校
6 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7f60679789d490b87dd90facdbde2ab.png)
(1)证明:函数
在
上单调递减;
(2)讨论关于x的方程
的实数解的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7f60679789d490b87dd90facdbde2ab.png)
(1)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa482d7bcaa385bfc3548b42a4bfb60.png)
(2)讨论关于x的方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfc0a91be1c6211ac53e0ca9dd8156b8.png)
您最近一年使用:0次
2023-05-12更新
|
554次组卷
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3卷引用:福建省福州延安中学2022-2023学年高二下学期会考第二次模拟考试数学试题
福建省福州延安中学2022-2023学年高二下学期会考第二次模拟考试数学试题(已下线)第05讲 4.5.1函数的零点与方程的解(2)-【帮课堂】浙江省S9联盟2022-2023学年高一下学期期中数学试题
名校
解题方法
7 . 已知函数
在
上单调递减,在
上单调递增.记函数
.
(1)写出函数
的单调区间(无需说明理由)及其最小值;
(2)若直线
与函数
和
的图象共有三个不同的交点,从左到右依次记为
,
,
,试证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d2399c2a712a2890dcd0b195d3b9f1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad2edd8edcb21bd41584daf9bb95a5c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6097169b69ad927c38efd7d52ec65f95.png)
(1)写出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af79f45b5880c72a349500da9d8e118d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c16dac1e9bf5804c8907cbc59014d04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6fbfe23e06cc72f33f925dd5ee3351e.png)
您最近一年使用:0次
8 . 已知函数
.
(1)若
,判断
的奇偶性(不用证明).
(2)当
时,先用定义法证明函数
在
上单调递增,再求函数
在
上的最小值.
(3)若对任意
,
恒成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e669169e561dc6b1baf0addb71c31fdd.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2f3b9d4e2c69fde9d77434b8b98e7a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200f24e682c93e02a87f3f9d57dc5d40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6d804ef44bfc64f824b0ccef71765e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6d804ef44bfc64f824b0ccef71765e.png)
(3)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b8c164755dc2d7cff80fb4c9cffc9be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
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9 . 在
)个实数组成的n行n列的数表中,
表示第i行第j列的数,记
,
若
∈
,且
两两不等,则称此表为“n阶H表”,记![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9f6f9fb93b7549faaa98d49b8b08ec7.png)
(1)请写出一个“2阶H表”;
(2)对任意一个“n阶H表”,若整数
且
,求证:
为偶数;
(3)求证:不存在“5阶H表”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79ff6f8857124f7bbc5a1c65c2e83767.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37a14c188b1c9d61aa237b137ba18023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10c9ff2b00c2841318b2697b070201a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c2fe368efe94c1e98309473e49a92fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37a14c188b1c9d61aa237b137ba18023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d253e22a1d9709dca48c6e0c649b47bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c0fdc4f349ea9634160ce08ac269691.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9f6f9fb93b7549faaa98d49b8b08ec7.png)
(1)请写出一个“2阶H表”;
(2)对任意一个“n阶H表”,若整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5db8c7f00e535ec1ffbb7008711b2096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8810a8ced3ca8dae09180a663275b425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(3)求证:不存在“5阶H表”.
您最近一年使用:0次
2023-03-14更新
|
870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北京市第一0一中学2023届高三数学统练三试题北京市第十一中学2023届高三三模(5月)数学试题(已下线)专题1 集合新定义题(九省联考第19题模式)练(已下线)微考点8-1 新高考新题型19题新定义题型精选
名校
解题方法
10 . 函数
是定义在
上的奇函数,且
.
(1)确定
的解析式;
(2)判断
在
上的单调性,并证明你的结论;
(3)解关于
的不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/970b7aecc3bf57efbbd1bdd18556cb40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cf664ed944afee2ec6d18b67fd09b06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1a62f443b896f5ae52f2d46015d59c0.png)
(1)确定
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cf664ed944afee2ec6d18b67fd09b06.png)
(3)解关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d06da5f9311195b66c3e8d1ecb90df3f.png)
您最近一年使用:0次
2023-05-05更新
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2227次组卷
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10卷引用:第三章 函数的概念与性质 讲核心 03
(已下线)第三章 函数的概念与性质 讲核心 03陕西省西安市铁一中学2022-2023学年高二下学期第3次月考文科数学试题天津市和平区2022-2023学年高二下学期期末数学试题(已下线)3.2+函数的基本性质-【冲刺满分】(已下线)3.2.2 函数的奇偶性(精讲)-《一隅三反》(已下线)第04讲 3.2.2奇偶性(精讲精练)(2)-【帮课堂】(已下线)第07讲 第三章 函数的概念与性质章末重点题型大总结(2)-【帮课堂】(已下线)专题04 函数导数综合应用(四大题型)-【好题汇编】备战2023-2024学年高二数学下学期期末真题分类汇编(天津专用)广西示范性高中2022-2023学年高一下学期联合调研测试数学试题云南省大理州祥云祥华中学2023-2024学年高一上学期二调考试(10月)数学试题