名校
解题方法
1 . 已知函数
在
上为奇函数,
,
.
(1)求实数
的值;
(2)指出函数
的单调性(说明理由,不需要证明);
(3)设对任意
,都有
成立;请问是否存在
的值,使
最小值为
,若存在求出
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8932f7d6ef4d9e276fdfd582d9fd9934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)指出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)设对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1fd4b6d54199a7ef857ecd2359c0f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb1359b9d7aac57284a7886ab2a7b1b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/459c84c9addfbd1cdd0a877ba7c584e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2022-09-29更新
|
804次组卷
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3卷引用:浙江省杭州第四中学吴山校区2021-2022学年高一上学期期末数学试题
浙江省杭州第四中学吴山校区2021-2022学年高一上学期期末数学试题(已下线)第5章 三角函数(基础、典型、易错、压轴)分类专项训练(2)福建省龙岩市长汀县第一中学分校2023-2024学年高一上学期第三次月考数学试题
名校
解题方法
2 . 已知函数
(
为自然底数).
(1)判断
的单调性和奇偶性;(不必证明)
(2)解不等式
;
(3)若对任意
,
,不等式![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00003eb6f472897ba1e4b4c1998be09e.png)
都成立,求正数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad2172d9c8b014c141fbf2b4d55704dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c04e8f899f16999d2068364f1b81e71.png)
(3)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5caabda288fc01cc168938846eec5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00003eb6f472897ba1e4b4c1998be09e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9897bf91ddaac9fa4121ab42ea7fdf45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2022-09-29更新
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818次组卷
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6卷引用:浙江省杭州第二中学滨江校区2021-2022学年高一上学期期末数学试题
3 . 设函数
.
(1)判断
的单调性;
(2)若方程
有两个相异实根
,
,求实数
的取值范围,并证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f53f81bca037a4383c1fab122a3cd3d.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/052ddf3664af9ab2990f3ea622997e00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a3ad8c843c361565d0f3cb06da49f60.png)
您最近一年使用:0次
名校
4 . 已知函数
.
(1)求
的解析式,并证明
为R上的增函数;
(2)当
时,
且
的图象关于点
对称.若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86363d44047e7a13439be95c5ada424f.png)
,对![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77b67e5c7a36a175b2af73c6cb4d1299.png)
,使得
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a86cefc2985d88b61b7bae760e83af76.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8d3f2fce683d1874c428ce8fb5e1a18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db8a4ff50485bfcdb95f887b17a0d157.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/355f79dcbb501ff9a8d8c1f8a3881572.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86363d44047e7a13439be95c5ada424f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a168bce0fa038163984ad5c48549268d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77b67e5c7a36a175b2af73c6cb4d1299.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef519a03bd4a93ce4ee046cdce14fbba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e63bbadc6250f7139836ede33205550.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
5 . 已知函数
为奇函数,
,其中
.
(1)若函数h(x)的图象过点A(1,1),求实数m和n的值;
(2)若m=3,试判断函数
在
上的单调性并证明;
(3)设函数
,若对每一个不小于3的实数
,都恰有一个小于3的实数
,使得
成立,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c905e72159af6fbe2d1931b75720e951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c4a4558290775d9fa439b4caf612c6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5132d6161e6aa7820232977ab3330fc.png)
(1)若函数h(x)的图象过点A(1,1),求实数m和n的值;
(2)若m=3,试判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c8e1101857a2373a3b9ba68bcfea910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/665945dcc8f5c0b8285a6ca4392ce7f6.png)
(3)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/556daa192145a8af678a1927ddf5b83c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e76ee3deb2f2a9d8bc418d38800f7cb.png)
您最近一年使用:0次
2022-03-27更新
|
889次组卷
|
10卷引用:湖南省长沙市明德中学2019-2020学年高一上学期期末数学试题
湖南省长沙市明德中学2019-2020学年高一上学期期末数学试题江苏省常州市第一中学2020-2021学年高一上学期期末数学试题(已下线)期末测试卷02(培优卷)-【满分计划】2022-2023学年高一数学阶段性复习测试卷(苏教版2019必修第一册)上海市复旦大学附属中学2018-2019学年高三上学期期中数学试题上海市复旦大学附属中学2019-2020学年高三上学期开学摸底数学试题上海市行知中学2020-2021学年高一上学期12月月考数学试题(已下线)4.2 指数函数-2021-2022学年高一数学尖子生同步培优题典(人教A版2019必修第一册)(已下线)第8章 函数应用(培优卷)-【满分计划】2022-2023学年高一数学阶段性复习测试卷(苏教版2019必修第一册)(已下线)专题07 函数恒成立等综合大题归类江苏省西安交通大学苏州附属中学2022-2023学年高一下学期开学考试数学试卷
名校
解题方法
6 . 已知函数
,函数
为R上的奇函数,且
.
(1)求
的解析式:
(2)判断
在区间
上的单调性,并用定义给予证明:
(3)若
的定义域为
时,求关于x的不等式
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ef8ceec2288e3485f893f8eae05fb07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51e817f37f5a814e856ebc4a16d676ce.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/455ba3d3e46977fcbe5b71f8bb9df4be.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/455ba3d3e46977fcbe5b71f8bb9df4be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c83a3106a7d6a2edd5baa29f0ba76b1c.png)
您最近一年使用:0次
2022-01-24更新
|
944次组卷
|
4卷引用:广东省梅州市2021-2022学年高一上学期期末数学试题
7 . 设
,函数
.
(1)若
,判断并证明函数
的单调性;
(2)若
,函数
在区间![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b85a97933a1d984f6e484b4021c800.png)
上的取值范围是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51f8ca3916770d199f7edd59b1722a86.png)
,求
的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c27b285c7ddbb366a8f1a183e2194ac1.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b85a97933a1d984f6e484b4021c800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/475963eea170ff0bbdaf2f0b706dfc34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51f8ca3916770d199f7edd59b1722a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06038810f4b137ab903256336b433b8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8573eecbc29f522671b3892ec406c50b.png)
您最近一年使用:0次
2022-01-21更新
|
674次组卷
|
2卷引用:浙江省杭州市八县区2021-2022学年高一上学期期末学业水平测试数学试题
名校
8 . 设
,函数
.
(1)若
,判断并证明函数
的单调性;
(2)若
,函数
在区间
(
)上的取值范围是
(
),求
的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5029bd373d0a619fd342eeb67a03dd2e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e10e1c43b86a8cd4360ca9b57232164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b85a97933a1d984f6e484b4021c800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb7961cbe98aac6a5fdee94582c341b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51f8ca3916770d199f7edd59b1722a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37b97b295f88972ba1c7e3cefda0885d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8573eecbc29f522671b3892ec406c50b.png)
您最近一年使用:0次
2022-02-16更新
|
773次组卷
|
4卷引用:广东省广州市天河区2021-2022学年高一上学期期末数学试题
名校
解题方法
9 . 已知函数
,
,其中
.
(1)
时,判断函数
的单调性(不需证明),并解不等式
;
(2)定义
上的函数
如下:
,若
在
上是减函数,当实数m取最大值时,求t的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb0e3b7384e7f0a324862c6589026b62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d0ea0821f8bb3cfbeab0bc5dab8c572.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48ae8d3e61598b3f81d3bd8a337c9801.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a2a51944c720568f35d443589dfc1aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d87d0e14d115dd37aa69f34602d3d4.png)
(2)定义
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6d804ef44bfc64f824b0ccef71765e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fa6a39515ef32c355c1a35be2da988c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e1ef4b55075ea0b421bae124a09614.png)
您最近一年使用:0次
2022-02-07更新
|
928次组卷
|
2卷引用:湖南师范大学附属中学2021-2022学年高一上学期期末数学试题
解题方法
10 . 若函数
满足
,则称函数
为“倒函数”.
(1)判断函数
和
是否为倒函数,并说明理由;
(2)若
(
恒为正数),其中
是偶函数,
是奇函数,求证:
是倒函数;
(3)若
为倒函数,求实数m、n的值;判定函数
的单调性,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdfaa3716ef9b13f4bdfe0b234df9932.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4508929da7db1adb7cc7a70e91be543.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dc9f0517304e39719c81d724ce2b860.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c118383937a12c505289f31b5d70a3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bde66f0ef8ea3ac6d6ac91a93ba69ae5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bde66f0ef8ea3ac6d6ac91a93ba69ae5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23b2373399a8dcbcfaa270d31e5e7bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/544f91d4fb22c571db9f8481b72a0419.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4211dfe3924d94e4b99f525e43a31cc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
您最近一年使用:0次