解题方法
1 . 已知函数
能表示为奇函数
和偶函数
的和.
(1)求
和
的解析式;
(2)利用函数单调性的定义,证明:函数
在区间
上是增函数;
(3)令
(
),对于任意
,都有
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04d938482f0bd0d62720f1175b128159.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(2)利用函数单调性的定义,证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed2f490aac02631c2ed9e6b76354a49.png)
(3)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6687058d9afa67f1f270d2a06b8b1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1e32125207addc3fdb92ceb0ec80ce8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ef17553c1d08bc53ef515daf8b51b82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
2 . 已知
是定义在
上的偶函数,对任意
,
且
,都有
,
,则不等式
的解集是( )
![](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/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1366beac4983dd04792fa87c9d8a8d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/717a1efcded39ade5c5e98eeb21013e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87a5c5e106845cc7549bc3473818d31f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8b03af66c2b6d916b41321d7bb292f1.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
3 . 设函数
,则满足
的
的取值范围为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab787250e9b5e148dfa63bd6eb7e1e55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3e21e5a556d8b208f2765684a70eca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
2024-02-03更新
|
571次组卷
|
3卷引用:江苏省南京市南京师大附中2023-2024学年高二上学期期末数学试题
江苏省南京市南京师大附中2023-2024学年高二上学期期末数学试题(已下线)专题07函数期末8种常考题型归类【好题汇编】-备战2023-2024学年高二数学下学期期末真题分类汇编(人教B版2019)河南省郑州市宇华实验学校2023-2024学年高二下学期开学摸底考试数学试题
解题方法
4 . 已知函数
是奇函数,则
的值为______ ;设
,若存在
,使
在区间
上的值域是
,则实数
的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c31230aac020a87222b4f54b7c25bc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78b5588afc52353ed599a3245135369a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b18edc6e2cea33c80b980949ed7d54f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d31e72421c0d65e00edb2acce12abffd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc3609700a12e22761fed5abfc5539a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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解题方法
5 . 已知函数
若
,则实数
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/417e1a12ad5a09282f11364fbaac56bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5d693df2793df615bbcb0343b5182f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() ![]() |
C.![]() | D.![]() ![]() |
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解题方法
6 . 已知定义在
上的偶函数
在区间
上单调递增.若
,则
的取值范围是__________ .
![](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/5ed2f490aac02631c2ed9e6b76354a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fddfeb64f006b3c2fa146454b1036009.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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名校
解题方法
7 . 已知函数
.
(1)若函数
为奇函数,求
的值;
(2)当
时,用函数单调性的定义证明:函数
在
上单调递增;
(3)若函数
有两个不同的零点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0dc17517b561f6196d2316faf55003.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef9f333cee2ccb2b215d93011a162f7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44e33629a5f5acd3cdd13747ef42a0eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2024-02-01更新
|
778次组卷
|
2卷引用:江苏省南京市2023-2024学年高一上学期期末学情调研测试数学试卷
名校
8 . 设函数
的定义域为
,其导函数为
,且满足
,
,则不等式
的解集为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64bbe1afc72a8561241d1b9bcd84aee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a085f038cc04a052a6afa2365833d419.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68bee4a8eb364e40b46773198bd93001.png)
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9 . 已知定义在
上的可导函数
的导函数为
,满足
且
为偶函数,
为奇函数,若
,则不等式
的解集为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/770f35b8dae2da2528c0961c4886ce20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25bacb5a64d4ae725bfcce99f0496dfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e81e15b871dd32b2438ef8025bcc42d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/497d358c288df6f5d30c4f29b94c3686.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e2c410654055712c72f25d1dc9edb91.png)
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2024-01-29更新
|
324次组卷
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4卷引用:江苏省盐城市盐城中学2023-2024学年高二上学期期末数学试题
江苏省盐城市盐城中学2023-2024学年高二上学期期末数学试题(已下线)6.2.1 导数与函数的单调性(2知识点+6题型+强化训练)-【帮课堂】2023-2024学年高二数学同步学与练(人教B版2019选择性必修第三册)(已下线)高二下学期期中复习填空题压轴题十五大题型专练-2023-2024学年高二数学举一反三系列(人教A版2019选择性必修第三册)四川省内江市资中县第二中学2023-2024学年高二下学期3月月考数学试题
10 . 已知函数
.(
是自然对数的底数)
(1)若
,
,求不等式
的解集;
(2)若
,证明:对任意
,
成立;
(3)若
,试讨论函数
的零点个数,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d974067fc61270a83b1320af368ba53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797bbd18359c9a29842b39109b3a0aac.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657435e1fda84118e7f63c97505c8b75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eec7d442dcd50c38bb6966d3822738f8.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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