名校
解题方法
1 . 已知
,函数
.
(1)若
有两个零点
,且
的最小值为
,当
时,判断函数
在
上的单调性,并说明理由;
(2)设
,记
为集合
中元素的最大者与最小者之差.若对
,
恒成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/331d5e308cd5469e0f28a8d75f79903f.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b3f51410d969f9fb41a595a028a6f06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0268e85df43d66b031e0eccb11284452.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f88a76f947e7022ef0c5efd6db060c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee3c6cdb19ac03dc3c28cd63b09dc907.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4802dfb4352b1162b6cda12fa469f91e.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebc20d351d51723c9b0a07a20ac14114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0225bca34eaf19544939b29153aac1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0e3589ab6dda85eb6dc9cab30878f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ff5474708041244835175778925a7ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8119e4e1c474bc2adbe014628043609.png)
您最近一年使用:0次
2022-01-23更新
|
375次组卷
|
3卷引用:重难点03函数(15种解题模型与方法)(4)
(已下线)重难点03函数(15种解题模型与方法)(4)山东省淄博市2021-2022学年高一上学期期末数学试题广东省东莞市东华高级中学、东华松山湖高级中学2023-2024学年高一上学期12月月考数学试题
解题方法
2 . 若函数
满足
,则称函数
为“倒函数”.
(1)判断函数
和
是否为倒函数,并说明理由;
(2)若
(
恒为正数),其中
是偶函数,
是奇函数,求证:
是倒函数;
(3)若
为倒函数,求实数m、n的值;判定函数
的单调性,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdfaa3716ef9b13f4bdfe0b234df9932.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4508929da7db1adb7cc7a70e91be543.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dc9f0517304e39719c81d724ce2b860.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c118383937a12c505289f31b5d70a3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bde66f0ef8ea3ac6d6ac91a93ba69ae5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bde66f0ef8ea3ac6d6ac91a93ba69ae5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23b2373399a8dcbcfaa270d31e5e7bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/544f91d4fb22c571db9f8481b72a0419.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4211dfe3924d94e4b99f525e43a31cc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
您最近一年使用:0次
解题方法
3 . 已知函数
的定义域为
,若存在常数
和
,对任意的
,都有
成立,则称函数
为“拟线性函数”,其中数组
称为函数
的拟合系数.
(1)数组
是否是函数
的拟合系数?
(2)判断函数
是否是“拟线性函数”,并说明理由;
(3)若奇函数
在区间
上单调递增,且
的图像关于点
成中心对称(其中
为常数),证明:
是“拟线性函数”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9eb0abfebb7bb39204e9aa051aa7f27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85899a6f573914e34170ea6b2e6b27cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)数组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad20e2bc6576fc461419f8f138d26e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/109d7264547e05af38ef2f36ec31f6d4.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/188074ba24ae37b38cc0c614a2274d88.png)
(3)若奇函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad7349dcd23527bce8da3e344459659.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/698c4d4e50062b4a7dd70fe1b4ab4fd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cd5371a6f0f82c65dd22f75f8b807c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
您最近一年使用:0次
名校
解题方法
4 . 已知函数
.
(1)求证:函数
是
上的减函数;
(2)已知函数
的图像存在对称中心
的充要条件是
的图像关于原点中心对称,判断函数
的图像是否存在对称中心,若存在,求出该对称中心的坐标,若不存在,说明理由;
(3)若对任意
,都存在
及实数
,使得
,求实数
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4077e55784510b6adc6a040daa85eb18.png)
(1)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30277e0be448b4955903e81e8795e45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c86212cfe7338ae7adca7d58eca15fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66b3ed9c4fa3bce5d45202695bbc179d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b55e9f87ebd16be23db0e9fea26da11a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e9fc70929247a1cdc2e8fc5c83df2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
2021-12-20更新
|
727次组卷
|
4卷引用:专题11 幂指对综合大题归类
名校
5 . 设
的定义域是
,在区间
上是严格减函数;且对任意
,
,若
,则
.
(1)求证:函数
是一个偶函数;
(2)求证:对于任意的
,
.
(3)若
,解不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d188ec2580e273ce87e51653a2177ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e11f4ca0e7ace69f92130d0525bcdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff565afbddafe8625ef376d7eb3fa649.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bc2435121b2b68da22ba4662e5734c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/333cf846facfab1283527ebe48961a95.png)
(1)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)求证:对于任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1591d4244dcf5539a4ae98f554e91e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5967cc62862986840af4dd29df4bcc41.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24f8b235e47a99a065a102c259b81db4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3059047431efe07f36b3fb319f709a78.png)
您最近一年使用:0次
2021-11-26更新
|
1209次组卷
|
5卷引用:专题03 函数的概念与性质(练习)-2
(已下线)专题03 函数的概念与性质(练习)-2(已下线)上海高一上学期期中【压轴42题专练】(2)(已下线)专题3-6 抽象函数性质综合归类(2) - 【巅峰课堂】题型归纳与培优练上海市复旦大学附属中学2021-2022学年高一上学期期中数学试题重庆市南开中学2022-2023学年高一上学期12月月考数学试题
名校
解题方法
6 . 对于定义在D上的函数
,若对任意
,不等式
对一切
恒成立,则称函数
是“A控制函数”.
(1)当
,判断
、
是否是“A控制函数";
(2)当
,
,
,若函数
是“A控制函数”,求正数m的取值范围;
(3)当
,
,D为整数集,若函数
是“A控制函数”且均为常值函数,求所有符合条件的t的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cc020b0997a2f37b214718112b79d8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a58fa30c7d315666eb9530242df7d09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20380b0bd02fec0e125d73d3fc6f202b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e88621b319f851a0b59e98f903efc1de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/199ec3824d5faac7eeec10f97c05b3e3.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfa3fb6bdded6d83b90d4852f5af85e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a20bfa0755dee91480f6a893ca71c230.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1b797b8d3ff68fc9ed63fdfb7e278ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8327d989f6a76682825e082b0fd5a2b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/406601b4c7d8ec573eab5e347bb2a4cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
您最近一年使用:0次
解题方法
7 . 已知函数
.在研究函数
的性质时,某同学发现:函数
的定义域为
,且
,所以函数
是偶函数.
(1)请沿着该同学的思路继续研究函数
的其他性质;
(2)若函数
在区间
上存在最大值和最小值,且最大值为
,请直接写出m的取值范围;
(3)若对
,函数
的图象都在直线
的上方,求k的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13d8f44731fc4a3d330f113d827c5da4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13d8f44731fc4a3d330f113d827c5da4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/384e43a54d9732f54927b5e587ba937f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)请沿着该同学的思路继续研究函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68f5688954bb4b46c94fe14a1cc6bdd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3627e4ccde7d69c49034a4a2d10bee5.png)
(3)若对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96b743603ab1c10330622f16db78dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fcf17d032f3e652e2b5cc50789bf3de.png)
您最近一年使用:0次