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
且
,证明:函数
必有局部对称点;
(2)若函数
在
上有局部对称点,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/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6197c1aa468bec795a0fbcc097cdc792.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6450ef54f5eb07e1961e2c76535944ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf10bf5b581a5826c48a1ba0b1d07529.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2023-12-12更新
|
543次组卷
|
3卷引用:上海市浦东新区上海海洋大学附属大团高级中学2023-2024学年高一上学期第二次月考数学试题
上海市浦东新区上海海洋大学附属大团高级中学2023-2024学年高一上学期第二次月考数学试题湖南省长沙市明德中学2023-2024学年高一上学期12月月考数学试题(已下线)第五章 函数的概念、性质及应用全章复习-【倍速学习法】(沪教版2020必修第一册)
解题方法
2 . 已知函数
为奇函数.
(1)求
的值;
(2)
,判断
的单调性(直接判断单调性,无需证明);
(3)当函数
的定义域为
时,若
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99ac26a92b91b1b813d26ae51586d427.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31cc2f18a4ad94b15cdea48d5de4fd78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(3)当函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09afe56172e6d35eade089aed201fcd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
名校
3 . 已知奇函数
满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/766af537003186e89784e2915d0a2812.png)
(1)求a,b的值并求
的值域:
(2)判断
的单调性(无需证明);
(3)若函数
恰有两个零点,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aab386a7ee3258bd65c9d5d10550ef3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/766af537003186e89784e2915d0a2812.png)
(1)求a,b的值并求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4e27fbe9557d2de1da83ba3a9770fc7.png)
您最近一年使用:0次
名校
解题方法
4 . 已知函数
=
(m
)是定义在R上的奇函数
(1)求m的值
(2)根据函数单调性的定义证明
在R上单调递增(备注:
>0)
(3)若对
,不等式
)
0恒成立,求实数k的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4026398c8ba0cab085e135835c213a6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f57b5a7c0283d2638c7b5a0baba4040.png)
(1)求m的值
(2)根据函数单调性的定义证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a29aa0e67c2e15d668e204d22501e3.png)
(3)若对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd039f8c34ce82079a017ba06ca738e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cdd59ab646e67b88446e36967f1cc3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e119c508fd265e3e3d78749e54fe4f43.png)
您最近一年使用:0次
2023-08-08更新
|
1136次组卷
|
4卷引用:天津市朱唐庄中学2022-2023学年高一上学期11月阶段性测试数学试题
5 . 已知函数
为偶函数
.
(1)求m的值;
(2)判断函数
在
的单调性,并证明你的结论;
(3)若函数
有四个不同的零点,求
取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3875bdd260f93849670759e51af6a8a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b00f32e1420c0dceaf59ca70b8ec2a5.png)
(1)求m的值;
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed2f490aac02631c2ed9e6b76354a49.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbd91d0a7f18b36493a7e90f77368253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
名校
解题方法
6 . 设A是正整数集的一个非空子集,如果对于任意
,都有
或
,则称A为自邻集.记集合
的所有子集中的自邻集的个数为
.
(1)直接写出
的所有自邻集;
(2)若
为偶数且
,求证:
的所有含5个元素的子集中,自邻集的个数是偶数;
(3)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/417abc71b8bee465746db0a35e776f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8ca2371b88985463ba25e4ec1ea453d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b377240e8ad277805e0499803d5be5e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(1)直接写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e47cd514b2920609e3781c87df6ab70.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/623eef12f37f0b85ddd367faa9b3bfad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5818ede14d21f6df9ef9c2bfe09286c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04aba3402e1d191ff96adda7c4af70ef.png)
您最近一年使用:0次
2023-05-28更新
|
708次组卷
|
11卷引用:北京市第二十中学2022-2023学年高二上学期12月月考数学试题
北京市第二十中学2022-2023学年高二上学期12月月考数学试题北京一零一中学2023届高三下学期数学统练四试题北京市东城区景山学校2024届高三上学期12月月考数学试题北京市第二中学2023-2024学年高二上学期12月第二学段考试数学试卷北京市西城区2021届高三5月二模数学试题北京市第五十七中学2021-2022学年高二上学期期中检测数学试题北京卷专题02集合(解答题)北京市第一0一中学2022-2023学年高三下学期统练数学试卷(四)(已下线)高一上学期第一次月考解答题压轴题50题专练-举一反三系列北京市北京师范大学第二附属中学2023-2024学年高二上学期期中测试数学试题(已下线)专题22 新高考新题型第19题新定义压轴解答题归纳(9大核心考点)(讲义)
解题方法
7 . 已知函数
的定义域为
,对任意
,都有
,且当![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e44c45ef0334070fc149b452dee26ae5.png)
时,
.
(1)求证:
是奇函数;
(2)若
,
对任意的
,
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b61bb7cb94b4d06f0090df1e365667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29a38999c26d3d60f7e431286686854e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49074b2fc18e7edb1b3b6b4e6f9737c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e44c45ef0334070fc149b452dee26ae5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa482d7bcaa385bfc3548b42a4bfb60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1a0169e37472db54391a8d175f8b2de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d472b21dde2c2afccb677f406d061e7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1591d4244dcf5539a4ae98f554e91e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10dd628a48cf11a09a49d38b40d1ce26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
名校
8 . 对任意给定的不小于3的正整数
,
元集合
均为正整数集的子集, 若满足:
①
;
②
;
③
,则称
互为等矩集.
(1)若集合
与
互为等矩集,求
的值;
(2)证明: 如果集合
互为等矩集,那么对于任意的正整数
,集合
也互为等矩集;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5debbaded2b2b268512d53339e460349.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b04f7ed829546d2b2260985f507f3a8.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b7bde3e3d8155e79ab1fa1fa9ee19f1.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea9a4259cca10c1f5af28e621ebafd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
(1)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12adcda385580201a896d40562dd497f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd0dc1dc5f1c10b956f04abde185490a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
(2)证明: 如果集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5debbaded2b2b268512d53339e460349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b454a8f5d20d6962b47c1c2508b1c16f.png)
您最近一年使用:0次
2023-10-17更新
|
160次组卷
|
2卷引用:上海市朱家角中学2023-2024学年高一上学期第一阶段质量检测数学试题
名校
解题方法
9 . 已知函数
的图象过点
,函数
,函数
.
(1)判断并证明函数
的奇偶性;
(2)若存在两不相等的实数
,使
,且
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5019c61adf61bd8c981b34ca3b8530f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdd9e314a9d0954be3d0a7b5191b316b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6923887353cdc0fe88d4b925c04b75ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02a877be8a1fe6a1a929f4c4139b5f33.png)
(1)判断并证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
(2)若存在两不相等的实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62ff2912fd8d93b6e692936d95b727c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7daeaf092342d6b164cd6783d148e586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a95382c6b3e5f9d85a5950bf85e029b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2023-04-21更新
|
330次组卷
|
2卷引用:江苏省南京市江浦高级中学等3校2022-2023学年高一下学期3月月考数学试题
名校
10 . 定义一个n元数组
,其中
或1,i、
﹐设
,
表示A和B中相应的元素不同的个数(例如,
,则
).
(1)若
,写出所有满足
的5元数组B;
(2)设
,记
的5元数组B的个数为
,求
的值;
(3)令
(n个0),
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/386216116ecf49be4a0ebdddacec60bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a70ee9f169cd7e6d36ddc301f2653498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f436426be5f021a8eebccc2298b6dea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce3b807eb2c7de7ec3a9bcf888b5caff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1411bda8a6dee80bb6387471cfe945bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092c1c15b9dfe25f62c33a23c63b9df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05ece890a7ada4782024dea0f592c14a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58aa6b0d8f54fa4ba22615db58834fc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02b44b19e29782883ea7a17ed0684154.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab88e3c1464bf1ec790168779faced2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59ce4001c7467ac929dd94288f6bce09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/545e6bd700ba1c9217f2c2598b459d4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c94707f5af06686f6265f2fdaa69b85.png)
(3)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4e725c235172819de9751e908e63ff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce3b807eb2c7de7ec3a9bcf888b5caff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f74fb4d2ac68691e607eb7c5cdf418ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5cc8f86e2046efa8b4f1dd5104b11c8.png)
您最近一年使用:0次