解题方法
1 . 已知定义在
上的函数
满足
,
,且
.
(1)求
的值;
(2)判断
的奇偶性,并证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e876debd1fc7a6f1f458c757f6e9f681.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01bc9c32ab68ddb51b1a4196f50081f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a32822a106d217ffdec43557a236f786.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
您最近一年使用:0次
2024-01-29更新
|
295次组卷
|
2卷引用:广东省珠海市大湾区2023-2024学年高一上学期1月期末联合考试数学试题
2 . 定义在
上的函数满足对任意的
,都有
,且当
时,
.
(1)判断函数
的奇偶性,并证明;
(2)判断
在
上的单调性,并用定义证明.
![](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/f58427d5aa7deeca47c8789241913f30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
(1)判断函数
![](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/d8b61bb7cb94b4d06f0090df1e365667.png)
您最近一年使用:0次
名校
解题方法
3 . 已知函数
对任意实数
恒有
,当
时,
,且
.
(1)判断
的奇偶性;
(2)判断函数单调性,求
在区间
上的最大值;
(3)若
对所有的
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/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab0c6f119137e1b6760d55956d99d963.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71baf6217604517fd98fa97d0f55b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91288f3376f00e3e4e37376c14f5c81d.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)判断函数单调性,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e99bebf8db0d314aacb2cb1f09bf48c.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26b851f738485e3326a196bd472c28d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38d838dbe2fac528f753ed46c431e86a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2023-12-03更新
|
527次组卷
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3卷引用:广东省东莞市四校2023-2024学年高一上学期12月期中联考数学试题
名校
解题方法
4 . 函数
对任意实数
恒有
,且当
时,
.
(1)判断
的奇偶性;
(2)求证:
是
上的减函数;
(3)若
,解关于
的不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be8e8e51ff9cf43529a75ce031f8865.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71baf6217604517fd98fa97d0f55b43.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/130ea481fadd167c198f6855bba2f654.png)
您最近一年使用:0次
2023-11-03更新
|
1516次组卷
|
3卷引用:广东省深圳市深圳大学附属实验中学2023-2024学年高一上学期期中数学试题
广东省深圳市深圳大学附属实验中学2023-2024学年高一上学期期中数学试题湖北省荆州市沙市中学2023-2024学年高一上学期11月期中数学试题(已下线)5.4 函数的奇偶性-【题型分类归纳】(苏教版2019必修第一册)
解题方法
5 . 定义在
上的单调函数
满足
且对任意x,
都有
.
(1)判断
的奇偶性,并说明理由;
(2)若
对任意
恒成立,求实数k的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fff8500d577a45550273be05fa62842.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f370a1d4dd341e5ab1774a66c66c1204.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab0c6f119137e1b6760d55956d99d963.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/296aba0e3514cce0478cd3b6ec0e8549.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
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2023-10-20更新
|
444次组卷
|
2卷引用:广东省深圳市科学高中2023-2024学年高一上学期期中考试数学试题
名校
解题方法
6 . (1)已知函数
,
,若
,都有
,求证:
为奇函数.
(2)设函数
定义在
上,证明:
是偶函数,
是奇函数.
(3)已知
是定义在
上的函数,设
,
,试判断
与
的奇偶性;根据
,
与
的关系,你能猜想出什么样的结论?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f41c7798e8266916b8501e3837194407.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e36e45821cc161584ad64043772227a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90c3cfb21d60dc4bea0083dbbba146c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1836fe79a57e10d585d267c50d67d421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8625e475c73bdfd992254680dc7d6b7f.png)
(3)已知
![](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/63c9abee0619dcc5cd3bf7f40c4edadd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca2ea8a2a6013eb18b53ea3aeb6ef56e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
您最近一年使用:0次
2023-08-20更新
|
252次组卷
|
2卷引用:广东省广雅中学2023-2024学年高一上学期期中数学试题
名校
解题方法
7 . 已知函数
对于任意实数
恒有
,且当
时,
,又
.
(1)判断
的奇偶性并证明;
(2)求
在区间
的最小值;
(3)解关于
的不等式:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c3c7d9a147725bd2ee363e3364b97b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab0c6f119137e1b6760d55956d99d963.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/249a976e88133f3b3733f09137cf5c42.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8254a9fe09d5e3940ad8c1c1c62c105c.png)
(3)解关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2516d9e181065fb6a0823d56c84be6fb.png)
您最近一年使用:0次
2023-02-17更新
|
1655次组卷
|
11卷引用:广东省中山市龙山中学2023-2024学年高一上学期10月月考数学试题
广东省中山市龙山中学2023-2024学年高一上学期10月月考数学试题重庆市永川北山中学校2022-2023学年高一上学期期末联考数学试题辽宁省鞍山市普通高中2022-2023学年高一下学期第一次月考数学(A卷)试题(已下线)3.2.2 函数的奇偶性(精练)-《一隅三反》(已下线)专题3.8 函数的概念与性质全章综合测试卷(提高篇)-举一反三系列(已下线)模块六 专题6 全真拔高模拟2湖北省荆州市沙市中学2023-2024学年高一上学期10月月考数学试题(已下线)第三章 函数的概念与性质(压轴题专练)-速记·巧练(人教A版2019必修第一册)四川省泸州市泸县第五中学2023-2024学年高一上学期11月期中考试数学试题(已下线)专题07 函数恒成立等综合大题归类(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
8 . 定义在区间
上的函数
,对
都有
,且当
时,
.
(1)判断
的奇偶性,并证明;
(2)判断
在
上的单调性,并证明;
(3)若
,求满足不等式
的实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d09dcbc6f4e0317fabb545af7d7c7fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2ba6e143efcc7436274fa619c996674.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/711d6e4d873ff21b365e9ed00982447a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
(1)判断
![](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/d562dc22dfb3b81d0c3f88b54d063c2f.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/241553167658572549705dda8cd7c207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c55d44fda81efe25ea99e98a26c0bd9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2022-12-20更新
|
1592次组卷
|
6卷引用:广东省佛山市顺德区国华纪念中学2023-2024学年高一上学期期中数学试题
名校
解题方法
9 . 定义在
上的函数
是单调函数,满足
,且
.
(1)求
的值;
(2)判断
的奇偶性,并证明;
(3)若对于任意
,都有
成立,求实数k的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/933093b52cca887f597cbe22a5467b11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c11f593161fd03dbfb19db890593e43f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0660e23f3be4f0f2b1d8e7f89fd68c.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f54b6a060d6c51a328341df76013bd89.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)若对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7020a6b646f85f77b4c58b3814b3426.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a64a2f163ccc97233f1a874f3b49ca4c.png)
您最近一年使用:0次
2022-11-12更新
|
571次组卷
|
3卷引用:广东实验中学越秀学校2022-2023学年高一上学期期中数学试题
解题方法
10 . 定义在
上的增函数
对任意
都有
.
(1)求证:
为奇函数;
(2)若对任意
,都有
恒成立,求实数
的取值范围
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5ab4b75fa22deba7fcbcdcb31dd45b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab0c6f119137e1b6760d55956d99d963.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb4955dcac5d61b8eae4e4d4a2517e2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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2024-01-07更新
|
376次组卷
|
2卷引用:广东省兴宁市黄陂中学2019届高三第一次月考数学试题