1 . 已知函数
,
.
(1)若函数
在
为增函数,求实数
的取值范围;
(2)当
时,
,函数
在区间
上的值域为
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da77594b6176f65b59863e02c144852e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c80cb910ebdc2457ef24e2b07b59af1a.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe86cace140f2c3588ab115837bbfc9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a882037b9ce104ecc496e0f31a139361.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a1c75ed22b86d7fae5b7ca9f34eb9b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9829ad49f32fb73dbde8d1d18ab3308e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/351629c193354cdcf202133052e45028.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a676bd44a087927c5878d0e8e9cdba13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2 . 已知函数
满足
,有
.
(1)求
的解析式;
(2)若
,函数
,且
,
,使
,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96b743603ab1c10330622f16db78dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab7ca79164d6a6e6834425f428c2bb29.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8befb6ffb9a4d955482b94ad9c7154f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b4dfad781aa9407473ea3c0980e6905.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab438a14d6afa5d8b4472f71d562bdd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bc9bbe373e92375f4aba21b828c9439.png)
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2卷引用:河南省三门峡市五县市2023-2024学年高一上学期1期末调研考试数学试题
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解题方法
3 . 已知函数
.
(1)判断
的单调性,并用单调性的定义证明;
(2)若对
,都有
成立,求实数
的取值范围;
(3)是否存在正实数
,使得
在
上的取值范围是
?若存在,求
的取值范围;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b586d5da50edf2b5d624b1f3368570eb.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99c7e73075eb82517587ea69bb59ecc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54237206e11b1e2423b91b92d4b4d05c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)是否存在正实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db527571cfd256c515424c6f9d114284.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88d1d51b4b335dc388d6c51bfd782047.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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2卷引用:山东省威海市2023-2024学年高一上学期期末考试数学试题
4 . 已知函数
,值域为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9a318701fb54b49b1f92283b74f026f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7f2c72ab559a0615db4c51327b78d4.png)
A.![]() | B.![]() |
C.![]() | D.![]() ![]() ![]() |
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5 . 已知函数
为奇函数.
(1)求
的值;
(2)若
在
上恒成立,求实数
的取值范围;
(3)设
,若
,使得
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e38371ea57658e033f41ddf5e51c91f1.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6278327c9a9968d1169ce3a125f2d3fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcac1e85463a3177f487d896b3d1d24c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7591504e793baf519c8b0e3ea8bfc508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88e47d4c4c6d534d98138e98474804ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f3bb43da17137e6c50874a8086df278.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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1055次组卷
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5卷引用:河南省许昌市2023-2024学年高一上学期期末教学质量检测数学试题
河南省许昌市2023-2024学年高一上学期期末教学质量检测数学试题上海市金山中学2023-2024学年高一下学期3月月考数学试卷辽宁省抚顺市第一中学2024学年高一下学期尖子班4月月考数学题江西省景德镇市乐平中学2023-2024学年高一下学期4月期中考试数学试题(已下线)专题02三角函数的图像与性质期末10种常考题型归类-《期末真题分类汇编》(人教B版2019必修第三册)
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6 . 已知函数
,
,若
,则
的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a16d2b46560259aff4d6948b7df0184.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9042a5a5abacdbe7fa173e7b5e9a0e41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e5665c5096027066a7d014dfc2cf148.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99d6b21a2a8b5adb0b0f8fd8632dc0c5.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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|
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3卷引用:浙江省嘉兴市2023-2024学年高一上学期1月期末检测数学试题
浙江省嘉兴市2023-2024学年高一上学期1月期末检测数学试题辽宁省沈阳市东北育才学校2023-2024学年高二实验部下学期阶段检测二(6月)数学试题(已下线)2024年新课标全国Ⅱ卷数学真题变式题6-10
解题方法
7 . 已知函数
是
上的偶函数,若
,则a的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fd2663d32c2434dbcb3d31140d90188.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf9768b9b3c0eb9e6edebae7a0d9bf0.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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8 . 设函数
,若对任意
,都存在唯一的
,使得
,则实数
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b205c44a76540af4a129e586e62d4ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b424bbc2f301c0ce92ed914fd49fa98c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/728697bd9af445ae7525af9168fdf816.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f5148c90b6d762234102e5bf5ca4c5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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解题方法
9 . 函数
的图象关于坐标原点成中心对称的充要条件是函数
为奇函数,可以将其推广为:函数
的图象关于点
成中心对称的充要条件是函数
为
关于
的奇函数,给定函数
,关于
中心对称.
(1)求
的值![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ca6fa9955690cec01db601e3abce0c.png)
(2)已知函数
,若对任意的
,总存在
,使得
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c7028a5fa4d781d382ca3b73b74796e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c7028a5fa4d781d382ca3b73b74796e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c7028a5fa4d781d382ca3b73b74796e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291aaad429837ab6dc1f99b9f7327cf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98f4cf449b51f221f9cb26e71a9dbebb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a42e14c5d826813dd33e04be2d2c26d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1f5fc756bf1aa3099dba53a6caba5a8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ca6fa9955690cec01db601e3abce0c.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae9dccd1d5763d4c2a8799ead64f475d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ee1e47231d0c468d7e2d720a0fdeee7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1247c1725b0a2037e53cbf5f7a668483.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9af9f0245165190c43c12ab642a97a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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解题方法
10 . 已知函数
在
上为奇函数,
.
(1)求实数m的值;
(2)存在
,使
成立.
(i)求t的取值范围;
(ii)若
恒成立,求n的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23db0aced2530841600107296baa0df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
(1)求实数m的值;
(2)存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc73297caf4c1813530134dc85080cdb.png)
(i)求t的取值范围;
(ii)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0da4a67544afb4c0edc031607e10cd91.png)
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