名校
1 . 对于定义域为D的函数y=f(x),如果存在区间[m,n]
D,同时满足:
①f(x)在[m,n]内是单调函数;
②当定义域是[m,n]时,f(x)的值域也是[m,n].则称[m,n]是该函数的“和谐区间”.
(1)证明:[0,1]是函数y=f(x)=x2的一个“和谐区间”.
(2)求证:函数
不存在“和谐区间”.
(3)已知:函数
(a∈R,a≠0)有“和谐区间”[m,n],当a变化时,求出n﹣m的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/637904facd16726fbfccb679e901e68a.png)
①f(x)在[m,n]内是单调函数;
②当定义域是[m,n]时,f(x)的值域也是[m,n].则称[m,n]是该函数的“和谐区间”.
(1)证明:[0,1]是函数y=f(x)=x2的一个“和谐区间”.
(2)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d3b0573a4ee2c68c86feda380291faf.png)
(3)已知:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a087c10b183ee28bc5fe1faa3289074.png)
您最近一年使用:0次
2016-12-04更新
|
1243次组卷
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8卷引用:上海市第二中学2022-2023学年高一上学期期末数学试题
名校
2 . 设
,已知函数
为奇函数.
(1)求实数
的值;
(2)若
,判断并证明函数
的单调性;
(3)在(2)的条件下,函数
在区间
上的值域是
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a6fe56c70ed96e7f0ee48063dae9fc7.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e10e1c43b86a8cd4360ca9b57232164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)在(2)的条件下,函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b605bf480dc152b67ebb9ebd96200b03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9449ab05d891f8607e82f9cf1dfab86c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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2022-12-14更新
|
990次组卷
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9卷引用:河南省新未来2022-2023学年高一上学期12月联考数学试题
河南省新未来2022-2023学年高一上学期12月联考数学试题河南省南阳市基础年级联合体2022-2023学年高一上学期12月月考数学试题河南省郑州市第四高级中学2022-2023学年高一上学期期末数学试题山西省朔州市2022-2023学年高一上学期12月月考数学试题河南省郑州市文华高级中学2023-2024学年高一上学期第三次月考数学试题河南省南阳市方城县第一高级中学2023-2024学年高一上学期期末模拟预测数学试题辽宁省朝阳市2023-2024学年高一下学期3月份考试数学试题云南省丽江市玉龙纳西族自治县第一中学2023-2024学年高一上学期12月月考数学试题云南省曲靖市马龙区第一中学2023-2024学年高一上学期期末考试数学试题
名校
3 . 对于定义域为D的函数
,如果存在区间
,使得
在区间
上是单调函数,且函数
,
的值域是
,则称区间
是函数
的一个“黄金区间”.
(1)判断函数
和函数
是否存在“黄金区间”,如果存在,请写出符合条件的一个“黄金区间”(直接写出结论,不要求证明);如果不存在,请说明理由.
(2)如果
是函数
的一个“黄金区间”,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5313c921defe84689aefde4773ad2b56.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/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a56806c9bf7927769af420fdabe96cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b85a97933a1d984f6e484b4021c800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b85a97933a1d984f6e484b4021c800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2892705d97580c9cf62d2ad04d48ec22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6672395f6806c5ece5d2625dda48a66.png)
(2)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b85a97933a1d984f6e484b4021c800.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5030281b8844165d690aa8431319d10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64da75a02173c2a5eb40f4c68d0f4f36.png)
您最近一年使用:0次
名校
4 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b047ffee43760a458d9c1d3740376ce2.png)
(1)利用函数单调性的定义,判断并证明函数
在区间
上的单调性;
(2)若存在实数
且
,使得
在区间
上的值域为
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b047ffee43760a458d9c1d3740376ce2.png)
(1)利用函数单调性的定义,判断并证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
(2)若存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42fd7af568e3d9f444beb0ff41426477.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/351629c193354cdcf202133052e45028.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a17639bec47bbb6843615094d87aa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2023-01-10更新
|
716次组卷
|
3卷引用:江苏省泰州市靖江高级中学2022-2023学年高一上学期期末数学试题
5 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a75f45372e0e53d12e7cacfa9810ce1a.png)
(1)若
是偶函数,
①求
的值;②判断函数
在
上的单调性并用定义证明.
(2)设
,若
值域为
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a75f45372e0e53d12e7cacfa9810ce1a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2313fbda01b873db01fe6add16df66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed2f490aac02631c2ed9e6b76354a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
名校
6 . 已知函数
.
(1)根据函数单调性的定义证明
在区间
上单调递减;
(2)若
在区间
上的值域为
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cdb6b28c106f33b7107bfb12eeccf07.png)
(1)根据函数单调性的定义证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/141f2ad9e03ece6b97f6b1d490c2e3e4.png)
(2)若
![](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/511579ec777132d680c253d52a6bac3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64da75a02173c2a5eb40f4c68d0f4f36.png)
您最近一年使用:0次
2022-11-03更新
|
847次组卷
|
6卷引用:湖南省湖湘教育三新探索协作体2022-2023学年高一上学期11月期中联考数学试题
湖南省湖湘教育三新探索协作体2022-2023学年高一上学期11月期中联考数学试题山东省青岛市2022-2023学年高一上学期期中数学试题(已下线)第二章 一元二次函数、方程与不等式单元测试(基础版)-【冲刺满分】(已下线)模块五 专题2 期中重组卷(山东)湖北省十堰市示范高中教联体测评联盟2023-2024学年高一上学期11月联考数学试题山东省滨州市惠民县2023-2024学年高一上学期期中数学试题
名校
解题方法
7 . 已知函数
是定义在区间
上的奇函数,且
,若对于任意的
,都有
.
(1)判断函数的单调性,并给出证明;
(2)若
,存在
,对于任意的
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ead3fdcb8fe8f5eb3dbe7d96cabc28b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0c9462c98381290a22e97c993ad7108.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c22fd64aea16406c6d1f8c4779aaecb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ef7f1625721af5314e8518f26c080e1.png)
(1)判断函数的单调性,并给出证明;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/982a6ec26dedf89e72ddaabfa6670183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24aa16b780156e18f12baa2b8ee0f9a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10dd628a48cf11a09a49d38b40d1ce26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
解题方法
8 . 已知函数
.
(1)直接写出
在区间
上的单调性(无需证明);
(2)求
在区间
上的最大值;
(3)设函数
的定义域为
,若存在区间
,满足:
,使得
,则称区间
为
的“
区间”.已知
,
是函数
的“
区间”,求实数
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca3fd09aa6bd2c73f713869a28e38e30.png)
(1)直接写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7fefece0cf6660a409832f72dff95.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c69d2c48ea2713321baf5d98342e50f.png)
(3)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e782887fa9cd8934bc19cc1288d5f51c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/921b9b04dd3678cba02ddc3f2c3f5298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0e83a3ae4472144b9626a1a443bd1bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca3fd09aa6bd2c73f713869a28e38e30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0c8ba627b98a0a528a63911c772302b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
9 . 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
10 . 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)
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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