名校
1 . 已知定义在
上的函数
满足:
.
(1)判断
的奇偶性并证明;
(2)若
,求
;
(3)若
,判断并证明
的单调性.
![](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/4ca24be2290ac9cf976edce22eb8d060.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/249a976e88133f3b3733f09137cf5c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4886e28e9ecd40f7edd25f25bde28453.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/146e32ccd4375d7898e8381ef7bee7f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a360203717effe5e60f78c5b2b7a95d.png)
您最近一年使用:0次
2024高一·全国·专题练习
解题方法
2 . 定义在
上的函数
是单调函数,满足
,且
,
.
(1)求
,
;
(2)判断
的奇偶性,并证明;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2628e2dd7a988cc80530e739c22b2280.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bede2686c931a3d8fa1de7cc086ec65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/104fc7daa1aaefd69764e2616109a4c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c12d4743a4c7c4401b31a44bb6ce959.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c60cf12a81b11e33356fe7e1c9e3d0b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/486e282537cf72c6908f7ecfa4ef4cee.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
您最近一年使用:0次
3 . 已知函数
的定义域是
,若对于任意
,都有
,且
时,有
.令
.
(1)求
的定义域;
(2)解不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ead3fdcb8fe8f5eb3dbe7d96cabc28b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f63cb59d5f3eb16beb379672fde5f170.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/eee3a00fbaf95e5647c79000f4c2eae5.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b17af43cc460a6a7010d51a0c9403d67.png)
您最近一年使用:0次
解题方法
4 . 已知定义域为
的函数
满足对任意
,都有![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e378c159436eb968d2b03eedd0e67657.png)
(1)求证:
是奇函数;
(2)设
,且当
时,
,求不等式
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff68d7374e6f548d902f18ed6b6e8c3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/243a45670e2b2fe44496d3244ed5a68d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e378c159436eb968d2b03eedd0e67657.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab409bb25958c2f01c73e26042c6f51e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0527a896aec4a245945e5edee00deed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/854e800115ee291759e0dbc95fdc43b2.png)
您最近一年使用:0次
名校
5 . 已知函数
,对于任意的
,都有
,当
时,
,且
.
(1)判断
的奇偶性和单调性;
(2)设函数
,若方程
有4个不同的解,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5ab4b75fa22deba7fcbcdcb31dd45b2.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/7b2a04e1a7a007001a5d9948a6dd82bc.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84b5d09845fc4e950cbb8d969d1c7aea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f86eff5761f61a20c240a428f2a7ceda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
解题方法
6 . 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
|
298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
名校
解题方法
7 . 已知定义在
上的函数
,对于
,恒有
.
(1)求证:
是奇函数;
(2)若
是增函数,解关于x的不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f70e0db0174a2c05b28fb6d0c2508778.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd384d86840b7b158af41f56fe29c7d1.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec1cdb84948a62fecaec0e17018ddf08.png)
您最近一年使用:0次
2024-01-21更新
|
603次组卷
|
4卷引用:辽宁省丹东市2023-2024学年高一上学期期末教学质量监测数学试题
解题方法
8 . 已知函数
满足以下几个条件
①
,
;②当
时,
;③
.
(1)求证:
为奇函数;
(2)解不等式:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3259a6def5ff390cf2f4e625294f95b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d43b263c92bb6d818fa5cdbe60bf66a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d87cd4403487962c38c8707ba3ab3fa3.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)解不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c47210b16df65ba9c28fa6b65114e87.png)
您最近一年使用:0次
解题方法
9 . 定义在
上的函数
满足
,且
不恒为0.
(1)求
和
的值;
(2)若
在
上单调递减,求不等式
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d028846b8614318fbf90387d13c75b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25bea6d14c16f7c06e4e028f36131360.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ce6155e181e21ce56ea658b70f8af17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a32822a106d217ffdec43557a236f786.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/402d65d46491910908c1ddc39a801cb5.png)
您最近一年使用:0次
10 . 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