1 . 已知函数
.
(1)若
,试写出函数
的值域(无需证明);
(2)若
,证明:
;
(3)已知
,且
恒成立,求
零点的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc2cd2c4133c7e847e203972dd209119.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b369eb031bad872b0d3a9cf746119f4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ece02a1eca34d876ca431b8b06d0d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c726d89e6bd2a1a5c6f682d752ab69e.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c726d89e6bd2a1a5c6f682d752ab69e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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解题方法
2 . 已知函数
为偶函数.
(1)求k的值;
(2)对任意
,存在
使得
成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39739af9b4cc09ee2a1227827dedd382.png)
(1)求k的值;
(2)对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53224898de85a85058ad336490bbbaa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c33e18e13664ff5a24b2145cd2b3509e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c72be96433ad5b2d206f7e7a91f6b138.png)
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2022-04-19更新
|
584次组卷
|
2卷引用:浙江省衢温“5+1”联盟2021-2022学年高一下学期期中联考数学试题
3 . 已知函数
是
上的奇函数,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34d11be133326fca264ac8a02879858d.png)
(1)求实数
,
的值,并求
的值域;
(2)函数
满足
,若对任意的
,不等式
恒成立,求实数
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34d11be133326fca264ac8a02879858d.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8ca5e821266f790bf9b8b851aa62b1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53224898de85a85058ad336490bbbaa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19948c7515e9f17bfdeaf1078a68e5c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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解题方法
4 . 已知函数
(a>0且
)是偶函数,函数
(a>0且
).
(1)求实数b的值;
(2)当a=2时,若
,使得
恒成立,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ef2b6d3b56799e1d8feb200f3d54693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a887738d524cc365eb6befcc6f8576bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf9d86203ddeaab06bdd2f634f1538dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
(1)求实数b的值;
(2)当a=2时,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46ef1801beb6ba3c9ba1ea800c7aa5d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a0f2a6631b90200440cea185a7fd059.png)
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2022-04-19更新
|
783次组卷
|
2卷引用:江苏省南京市中华中学2021-2022学年高一下学期4月阶段检测数学试题
名校
5 . 在①
,②
这两个条件中任选一个,补充到下面问题的横线中,并求解该问题.已知函数
.
(1)当
时,求函数
在区间
上的值域;
(2)若______,
,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c18946c8631ebbbf47a0fc02f4ba7b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7780f324bba98e6bf3218daf3e8f8d58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c32f6ecd5ec87b309611bcf7e623aa.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f22a4a0dd7307a1323d25331e60782d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ead3fdcb8fe8f5eb3dbe7d96cabc28b.png)
(2)若______,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
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2022-08-30更新
|
739次组卷
|
14卷引用:安徽省蚌埠市2020-2021学年高一上学期期末数学试题
安徽省蚌埠市2020-2021学年高一上学期期末数学试题江苏省扬州中学2020-2021学年高一下学期开学考试数学试题广东省惠州市龙门县高级中学2021-2022学年高一上学期11月中段测试数学试题福建省泉州市五校联考2021-2022学年高一上学期期中考试数学试题北师大版(2019) 必修第一册 名校名师卷 专题三 函数2023版 北师大版(2019) 必修第一册 突围者 第二章 第三节 函数的单调性和最值福建省厦门第二中学2022-2023学年高一上学期第一次月考数学试题辽宁省沈阳市东北育才学校高中部2022-2023学年高一上学期开学摸底考试数学试题2.3 函数的单调性和最值同步练习-2022-2023学年高一上学期数学北师大版(2019)必修第一册3.2.1 函数的单调性与最值 课时练习(已下线)3.2.1 单调性与最大(小)值——最值(第2课时)(分层作业)-【上好课】江苏省盐城市响水中学2023-2024学年高一上学期期中考试数学试题(已下线)培优专题01 二次函数含参数最值问题-【同步题型讲义】(人教A版2019必修第一册)湘鄂冀三省益阳平高学校、长沙市平高中学等七校2022-2023学年高二上学期10月联考数学试题
6 . 已知函数
.
(1)求
的最小正周期;
(2)若关于x的不等式
在
上恒成立,求实数m的取值范围.
(注:可能用到的结论:
在
上是增函数)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e30f2717961e9da64b59b3989c6c4c2.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若关于x的不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9af5fddab05b03313fe991e1c6f2034.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
(注:可能用到的结论:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10f950c76261d724c280c686c6cf220a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/417ab20883d799aaf311371393fa7d7c.png)
您最近一年使用:0次
名校
7 . 已知函数
(
,
)是奇函数.
(1)若
,对任意
有
恒成立,求实数
的取值范围;
(2)设
(
,
),若
,问是否存在实数
使函数
在
上的最大值为0?若存在,求出
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fa28501b76696dd6e1ab8ad83b33d64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ad8c8165036178e5ca51d0a7c2b3a67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3993391fe16e7315c4d92af28c03fa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305c82799c4a08c2c6b1aac3aa5c9423.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7e2fc9cebff67c6d256cc75ce86dd60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/060e7930731eddbcfac592b808e9b698.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd0e5e3f3477931e7c15cf609b422410.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e03ad0c315806342d6cd732a0b91a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6602b172fa321eacd584c338dee7bef8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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8 . 已知函数
,
,
,其中
表示a,b中最大的数.若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d08717f13c81d35e5e1ca03d09f0de8.png)
________ ;若
对
恒成立,则t的取值范围是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/981bef8467438139eff0195685fd634b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/558c16b4a752c61e60a9d9a974d83d30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7225c625819b7bfeb393a377ec2d74a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee9d48e670be1ddbfee3738824a7eccf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a2a51944c720568f35d443589dfc1aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d08717f13c81d35e5e1ca03d09f0de8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4561a8be31924a8c25169873501b3b3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
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2023-05-31更新
|
482次组卷
|
4卷引用:北京市第一六一中学2022-2023学年高一上学期12月阶段练习数学试题
名校
解题方法
9 . 已知函数
,其中b∈R.
(1)若m=b=2,且
时,f(x)的最小值是-2,求实数a的值;
(2)若m=2,0<a<1,且
时,f(x)≤0恒成立,求实数b的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1b95aebe9dbf4f2909fdc197fa24697.png)
(1)若m=b=2,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/506dafea10a6946d23c2ed2f7997cd3f.png)
(2)若m=2,0<a<1,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/506dafea10a6946d23c2ed2f7997cd3f.png)
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解题方法
10 . 函数
.
(1)若
,
,求函数
的值域;
(2)当
,且
有意义时,
①若
,求正数
的取值范围;
②当
时,求
的最小值
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81d4011533b6c50a7387f2c85a4f7bcc.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f02fe0ecf85e515ee38e6c1337357932.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a34b4bf4bba566959635a7982cec6ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99729b874d144465b56fb11fcf92503e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecf9befc3b336d83b83bcfcbc19c0752.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d09a2b7c019dae83e027830b82b3ee8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
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