名校
1 . 设函数
的定义域为
,对于区间
(
,
),若满足以下两条性质之一,则称
为
的一个“美好区间”.性质①:对任意
,有
;性质②:对任意
,有
.
(1)判断并证明区间
是否为函数
的“美好区间”;
(2)若
(
)是函数
的“美好区间”,试求实数
的取值范围;
(3)已知定义在
上,且图像连续不断的函数
满足:对任意
(
),有
.求证:
存在“美好区间”,且存在
,使得
不属于
的任意一个“美好区间”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2f15034a908e359bed8b5e0cc467b9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a46e678bf9d2df5ad4c782b3dc22f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e31b14d5b4da0298a7dea660b03d1066.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bb6324279df94decba955e04ccfa9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c1e560364dea022693928309250f158.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bb6324279df94decba955e04ccfa9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/494d4b56c165f3bd6d41ea80dddc6b71.png)
(1)判断并证明区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6c1756b564bf1d998d8179637011c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb68ccf2d913a83e68df3524263aa8dd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbae0d22d931ac42b565c7990764a2c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd8ed92f58d44ee590c425bc741195c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)已知定义在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73254f32b6da29ecc32df2e9f87a4c97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a46e678bf9d2df5ad4c782b3dc22f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/792349a458f6b6d3905775978ee05818.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/070054c0b4182ab7399ed56925844e93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
您最近一年使用:0次
名校
解题方法
2 . 已知定义在
上的函数
满足
,且当
时,
.
(1)求
的值,并证明
为奇函数;
(2)求证
在
上是增函数;
(3)若
,解关于
的不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/933093b52cca887f597cbe22a5467b11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbc2ae509aed37fd2e2c8faa640ab231.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1c3f4162ae5563b2c9737d0979b1926.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e38fffbc7ab9882480f4faa72390e23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39d43e46dba47f1543056c1e376e16ab.png)
(2)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/933093b52cca887f597cbe22a5467b11.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ed670b1f668778c6243f3f7470ee7d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9521a6482b63d10996088eec2c7f1083.png)
您最近一年使用:0次
2023-10-12更新
|
2008次组卷
|
4卷引用:辽宁省大连市育明高级中学2023-2024学年高一上学期期中考试数学试卷
名校
解题方法
3 . 函数
是定义在
上的奇函数,且
.
(1)求
的解析式;
(2)证明
在
上为增函数;
(3)解不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fd83b37f8979128b120e5b5af803b3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/455ba3d3e46977fcbe5b71f8bb9df4be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffc6da8cf1ccead63fcacc383560e0ba.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/455ba3d3e46977fcbe5b71f8bb9df4be.png)
(3)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d06da5f9311195b66c3e8d1ecb90df3f.png)
您最近一年使用:0次
2023-12-16更新
|
476次组卷
|
4卷引用:辽宁省朝阳市2023-2024学年高一上学期期中数学试题
名校
解题方法
4 . 已知函数
.
(1)用定义证明
是
上的增函数.
(2)是否存在m,使得对任意的
恒成立?若存在,求出m的取值范围;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b586d5da50edf2b5d624b1f3368570eb.png)
(1)用定义证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
(2)是否存在m,使得对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce5e41c8ad37efd3b0f1d07423a7ea9c.png)
您最近一年使用:0次
2023-11-28更新
|
667次组卷
|
3卷引用:辽宁省葫芦岛市协作校2023-2024学年高一上学期第二次考试数学试题
名校
解题方法
5 . 已知定义域为
的函数
满足对任意
,都有
.
(1)求证:
是偶函数;
(2)设
时
,
①求证:
在
上是减函数;
②求不等式
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff68d7374e6f548d902f18ed6b6e8c3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73f8ddd9ec2c31da2222ef499187029a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b23478a1fcd7ba7a2a7adc61f20b1d6b.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71baf6217604517fd98fa97d0f55b43.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
②求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a56ae3279b9aabb43dc9e1b0724fbcf.png)
您最近一年使用:0次
2023-09-29更新
|
1925次组卷
|
12卷引用:辽宁省沈阳市东北育才学校科学高中部2023-2024学年高一上学期期中数学试题
辽宁省沈阳市东北育才学校科学高中部2023-2024学年高一上学期期中数学试题(已下线)专题03 函数的概念及性质(测)(已下线)高一上学期期中考试解答题压轴题50题专练-举一反三系列(已下线)专题3-6 抽象函数性质综合归类(1) - 【巅峰课堂】题型归纳与培优练山东省泰安市泰山中学2023-2024学年高一上学期期中数学试题广东省佛山市南海区2023-2024学年高一上学期S7联考考前模拟训练数学试题云南省曲靖市罗平县第一中学2019-2020学年高一上学期期中数学试题2020届百校联盟TOP300八月尖子生联考(全国I卷)文科数学试题2020届百校联考高考考前冲刺必刷卷(三)全国I卷数学(文)试题贵州省思南中学2020-2021学年高一上学期第一次月考数学试题(已下线)专题07 《函数概念与性质》中的解答题压轴题(1)-2021-2022学年高一数学上册同步培优训练系列(苏教版2019)福建省莆田市擢英中学2022-2023学年高一上学期期中数学试题
名校
解题方法
6 . 已知函数
是定义在
上的偶函数
(1)写出实数
满足的条件.
(2)利用函数单调性定义证明
在
单调递增.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/201f1d68ba740bdfa6732cf51a28f1f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
(1)写出实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
(2)利用函数单调性定义证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
您最近一年使用:0次
名校
解题方法
7 . 已知函数
,
.
(1)若函数
在
上为偶函数,试求实数
的值;
(2)在(1)的条件下,当
的定义域为
时,解答以下两个问题:
①判断函数
在定义域上的单调性并加以证明;
②若
,试求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a53225a4474f496c872da423a7de9fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49f15aa143c8c66bb676bfccc68f8ec6.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/004ccc72ce2d293699c9ca7b0f600786.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)在(1)的条件下,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/455ba3d3e46977fcbe5b71f8bb9df4be.png)
①判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a352d7f5ea4b315b3896ace49b574a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
名校
解题方法
8 . 已知函数
.
(1)若
,判断
的奇偶性并加以证明.
(2)若
时,不等式
恒成立,试求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc1129146b14c08d9945d001a8aff0fe.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35821eae71dfea3b136fe7ee19944a37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f2d760365bd601de949e86826208f31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14ce02fdd55b324bc19bacbd5545f76e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
解题方法
9 . 已知函数
,
.
(1)当
时,求函数
的单调递增区间(不必写明证明过程);
(2)判断函数
的奇偶性,并说明理由;
(3)当
时,若对任意的
,恒有
成立,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25b5a833ef31325cf5f23446913a6bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b89c33bf8803c80b65d4ebd7746645e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/998485ffeb46a0412ff1a0f814429257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/911ef39b13a09894783851f7da24c1a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/163836ab07d982556c85ac2e6a13ae72.png)
您最近一年使用:0次
名校
解题方法
10 . 已知定义域为
的函数
是奇函数.
(1)判断
单调性,并用单调性的定义加以证明;
(2)若不等式
对任意的
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef9f333cee2ccb2b215d93011a162f7a.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46a79b8a0da3c3dea07b81e7365da5af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次