1 . 已知函数
.
(1)求该函数的定义域,并证明其为奇函数;
(2)判断函数
在
上的单调性,并说明理由;
(3)对于任意
,不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f2d08cc0467eeb8d4fcf4d876729967.png)
(1)求该函数的定义域,并证明其为奇函数;
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02e1c9c97de9198d47306216e9961b80.png)
(3)对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9186dc3f15560a1e10970193893e9f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a3fc9c353fd2e294d615fc5b4f3914.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
名校
解题方法
2 . 若函数
满足:对任意正数
,都有
,则称函数
为“H函数”.
(1)试判断函数
与
是否为“H函数”,并说明理由;
(2)若函数
是“H函数”,求实数a的取值范围;
(3)若函数
为“H函数”,
,对任意正数s、t,都有
,
,证明:对任意
,都有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b056a90a2751f04ba5fff3dc5c1d0674.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17dfefdc8541c51ae463de8b36086374.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)试判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a04e15196ce905f578e53b845242ee30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce0793207b5a6162ba631291f6598bb5.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36f51c8abc2b4eddcbb2ff770c74f62d.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/249a976e88133f3b3733f09137cf5c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4028ed0e84791a6da036d71af685b63d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5afc7ce5b1f3ac621c3bc08b4e243278.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ddd19fd5d1d779501b8adecaf3e938d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/219598f1289ddb370d632ea141731d52.png)
您最近一年使用:0次
名校
解题方法
3 . 函数
的定义域为
,若存在正实数
,对任意的
,总有
,则称函数
具有性质
.
(1)判断下列函数是否具有性质
,并说明理由.
①
;②
;
(2)已知
为二次函数,若存在正实数
,使得函数
具有性质
.用反证法证明:
是偶函数;
(3)已知
,
为给定的正实数,若函数
具有性质
,求
的取值范围.(用
表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a380348dd1544f954255976659a84a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daac43c7675fa411b35028e09b0bad90.png)
(1)判断下列函数是否具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2387880727d458702651d699e76d7d76.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a800cbb4978417d9536f19bc0dbf5a29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4306fb6d5419322b4b7b9140e06e43a0.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daac43c7675fa411b35028e09b0bad90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/478cfa8c1cbab3781ff7b81be74d4c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daac43c7675fa411b35028e09b0bad90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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名校
解题方法
4 . 设集合
存在正实数
,使得定义域内任意x都有
.
(1)若
,证明:
;
(2)若
,且
,求实数a的取值范围;
(3)若
,且
,求函数
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76a293f8a5cb9cb0d905ca25a01faefc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b452eaa74ef4e90a6661350333df7e49.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/318a16f1950d06e5500c76d8f81a507f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efb1ba12c3538ad16ac98407658246f0.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/021f43d4d536af9301adad72758d3355.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764df344e05f8ef1a97b346ddf44a5a0.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7974d7d586f9697ad00b34ce5ada820.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9511a2031188decf655cdfc0302b4740.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e915b67f8f747698b8b46d37bc453667.png)
您最近一年使用:0次
解题方法
5 . 已知函数
.
(1)求函数的定义域;
(2)求证:
是奇函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97d44c9fbbc4f7810ba9525fb5d0f577.png)
(1)求函数的定义域;
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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解题方法
6 . 对于函数
,函数图象上任意一点A关于点P的对称点
仍在函数图象上,那么称点P为函数图象的对称中心.如果
足够大时,图象上的点到直线
的距离比任意给定的正数还要小,那么称函数图象无限趋近于该直线
,也称直线
是函数图象的非垂直渐近线.
(1)研究函数
的性质,填表但无需过程:
(2)根据(1),在所给的坐标系中,画出大致图象,如有对称中心,则在图象中标为点P,如有非垂直渐近线,用虚线画出;
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/11/9666ea8a-c948-4c6b-87d0-fb09cc31a56f.png?resizew=288)
(3)由(1)(2),选择以下两个问题之一来答题.
①如果函数
的图象有对称中心,请根据题设的定义来证明,如果没有,请说明理由;
②请根据题设的定义,证明:函数
的图象在x轴上方,且无限趋近于x轴,但永不相交.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe916d05211cf74a2b1428a8bb8bbbbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(1)研究函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df7c3338bd45a8a412b672118e8aea7d.png)
值域 | |
单调性 | |
奇偶性 | |
图象对称中心 | |
图象非垂直渐近线 |
(2)根据(1),在所给的坐标系中,画出大致图象,如有对称中心,则在图象中标为点P,如有非垂直渐近线,用虚线画出;
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/11/9666ea8a-c948-4c6b-87d0-fb09cc31a56f.png?resizew=288)
(3)由(1)(2),选择以下两个问题之一来答题.
①如果函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
②请根据题设的定义,证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
您最近一年使用:0次
2023高一上·上海·专题练习
解题方法
7 . 已知函数
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07e2c65e48a576287843976a738fb4f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32d6b59f4796a45963dea76b89c72bea.png)
您最近一年使用:0次
2023高一上·上海·专题练习
8 . 求函数
的反函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41f86d8967ac85000c7032ac9fa1f2e2.png)
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2023高一上·上海·专题练习
解题方法
9 . 已知函数
的定义域为R,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52da4c2ec000a570bfa9635f5159b382.png)
您最近一年使用:0次
2023高一上·上海·专题练习
解题方法
10 . 求下列函数的定义域
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2efc9ca1dd832193a2e7f94fe371294.png)
(2)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2efc9ca1dd832193a2e7f94fe371294.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20e589743388784e13a39dbe11cd63f7.png)
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