名校
1 . 设函数
.
(1)求
的值;
(2)判断函数
的奇偶性并证明;
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fa6886b6b9df83a5942cdb0c7017539.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e0a99715731d8dccd5fd0c77abbd9e3.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6853d01dfa3c24c7a5bf9ad0b026567d.png)
您最近一年使用:0次
2021-11-16更新
|
200次组卷
|
2卷引用:广东省广州市番禺区实验中学2021-2022学年高一上学期期中数学试题
名校
解题方法
2 . 已知函数
对任意x,
,总有
,且当
时,都有
成立,且
.
(1)求证:函数
是奇函数;
(2)利用函数的单调性定义证明
在R上单调递减;
(3)若不等式
对任意的
恒成立,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54dad48527a47eab4a5916ab0421cc71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a80f7e98cf9a07b94f192668f3063a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e520c1ab44faaa476a5f3f6181db0f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af1fd20e2187be1e00c4c5343eccd0c8.png)
(1)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
(2)利用函数的单调性定义证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
(3)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/865ea9d9334865ba6778b6191b32bbf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f2b6c88755ed1b75b5adb7c01060946.png)
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2021-10-28更新
|
885次组卷
|
3卷引用:内蒙古赤峰二中2021-2022学年高一上学期第一次月考数学(理)试题
名校
解题方法
3 . 设
,函数
.
(1)若
,求证:函数
是奇函数;
(2)若
,判断并证明函数
的单调性;
(3)设
,
,若存在实数m,n(
),使得函数
在区间[m,n]上的取值范围是
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d04bcc342e046321abc203690916602.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b29a7faa14a6e09d0db2d04f4ced03.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e10e1c43b86a8cd4360ca9b57232164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b29a7faa14a6e09d0db2d04f4ced03.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44a4eaa80b44625890339d6a0065c241.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb7961cbe98aac6a5fdee94582c341b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b29a7faa14a6e09d0db2d04f4ced03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d45cf196f21e10ce4031d26fefc22f56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8573eecbc29f522671b3892ec406c50b.png)
您最近一年使用:0次
2022-01-21更新
|
714次组卷
|
8卷引用:江苏省南通市通州、海安2019-2020学年高一上学期期末联考数学试题
江苏省南通市通州、海安2019-2020学年高一上学期期末联考数学试题(已下线)【新东方】在线数学35江苏省南通市通州区金沙中学2020-2021学年高一上学期第二次调研考试数学试题上海市控江中学2021-2022学年高一上学期期末数学试题四川省四川师范大学附属中学2021-2022学年高一上学期12月月考数学试题(已下线)第13讲 函数的基本性质(8大考点)(3)(已下线)第13讲 函数的基本性质(8大考点)(2)(已下线)专题14函数的基本性质-【倍速学习法】(沪教版2020必修第一册)
4 . 已知集合
,且
.
(1)判断
是否为
中元素
(2)设
,求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ca653cad7e7730a8e03b55d0cd1a85.png)
(3)证明:若
,则
是偶数;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bf7926d4460da0d09ebab079fdc13e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d72bf44a312d976cb458311c73b7fb7.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35f3aa35fae3f1e1afdd5386c172d517.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac385ec112e6d61b90d953e3f106ee85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ca653cad7e7730a8e03b55d0cd1a85.png)
(3)证明:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13f40c24c64bbb0645fcf585f4e66872.png)
您最近一年使用:0次
解题方法
5 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeccfff03711ca585eb358459dc68107.png)
(1)求证:用单调性定义证明函数
是
上的严格减函数;
(2)已知“函数
的图像关于点
对称”的充要条件是“
对于定义域内任何
恒成立”.试用此结论判断函数
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/eeccfff03711ca585eb358459dc68107.png)
(1)求证:用单调性定义证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
(2)已知“函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a8319f56cfb802b0e049b4765b5ec79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4003115706a191f2d4415119e73ddaa1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9902484b765fe634029040cc5dae6cfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c8ef8cdf661a9557e490588ef45dcfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
名校
6 . 已知函数
.
(1)求
;
(2)判断函数的奇偶性,并加以证明;
(3)求证:函数在
上单调递减.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f856cd620c2538680d2b272269d6559.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/981b2f8d56d6629da4eb1fc8a701fb9a.png)
(2)判断函数的奇偶性,并加以证明;
(3)求证:函数在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8938db94f49dcbe0c383fba0241bb0da.png)
您最近一年使用:0次
名校
7 . 已知函数
.
(1)判断函数
的奇偶性,并证明;
(2)求证:
在
上单调递减.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d102f257b33791eb0fa9571b1bcf13f.png)
(1)判断函数
![](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/6ab5e0524def52baf53480b8726784ed.png)
您最近一年使用:0次
名校
8 . 设
,函数
.
(1)已知
,求证:函数
为定义域上的奇函数;
(2)已知
.
(i)判断并证明函数
的单调性;
(ii)函数
在区间
上的值域是
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5029bd373d0a619fd342eeb67a03dd2e.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e10e1c43b86a8cd4360ca9b57232164.png)
(i)判断并证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(ii)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/711e45f600c091e6830c0b70cd012ca3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16ff0183cc03b2dd1262139df3b646b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8573eecbc29f522671b3892ec406c50b.png)
您最近一年使用:0次
9 . 若对于任意
,
,使得
,都有
,则称
是W陪伴的.
(1)判断
是否为
陪伴的,并证明;
(2)若
是
陪伴的,求a的取值范围;
(3)若
是
陪伴的,且是
陪伴的,求证:
是
陪伴的.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ba8542fbe02e78cf3948c9abea9855.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5c93e9660a396fa4480011de15077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daef57e451456c817f2f64cffe42a73d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b672f564d03ed46d092bb130f229ad8.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c124b1e1e7241cc507a351bcd1f273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e70124e83e169692d19cc8d3c2e924ea.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0c6c52b42a8404031b97d71ed6a1b23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e70124e83e169692d19cc8d3c2e924ea.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b672f564d03ed46d092bb130f229ad8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b378c027964a5f51a6b004bae5b2d0bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce700a387c89497f5c98889881a735c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b672f564d03ed46d092bb130f229ad8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0f0d82308db0868690c7d65935b79ae.png)
您最近一年使用:0次
2021高一·上海·专题练习
解题方法
10 . 设函数
是定义在
上的偶函数,且
对任意的
恒成立,且当
时,
.
(1)求证:
是以2为周期的函数(不需要证明2是
的最小正周期);
(2)对于整数
,当
时,求函数
的解析式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/545931b962cf570712d04888b57093f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1376168658dbe7f5b7f4d75fb1db545a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/318a16f1950d06e5500c76d8f81a507f.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)对于整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1300fc4664b019bef578d4500b401b7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
您最近一年使用:0次
2021-08-31更新
|
333次组卷
|
3卷引用:第13讲 函数的对称性与周期性-【提高班精讲课】2021-2022学年高一数学重点专题18讲(沪教版2020必修第一册,上海专用)
(已下线)第13讲 函数的对称性与周期性-【提高班精讲课】2021-2022学年高一数学重点专题18讲(沪教版2020必修第一册,上海专用)(已下线)第5章 函数概念与性质 单元综合检测(难点)(单元培优)-2021-2022学年高一数学课后培优练(苏教版2019必修第一册)(已下线)第五章 函数的概念、性质及应用(6大易错与5大拓展)(2)-单元速记·巧练(沪教版2020必修第一册)