名校
1 . 已知函数
.
(1)利用函数单调性的定义,证明:
在区间
上是增函数;
(2)已知
,其中
是大于1的实数,当
时,
恒成立,求实数
的取值范围;
(3)当
,判断
与
的大小,并注明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2cab732f2937104d04a0a40d7efbf66.png)
(1)利用函数单调性的定义,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed2f490aac02631c2ed9e6b76354a49.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/516411862c4dc7ceac5d36510d460d32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e884ea16357b019cb4be0fe722de69c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c04bd9759565e4cd93839a2ce2b31b51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce3a34d6f60032718820c3da2b07786b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2226e39e890e8d985f6fdfe478827400.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fda584797f3f952ac549b8bb0d76a660.png)
您最近一年使用:0次
解题方法
2 . 已知函数
.
(1)判断
的单调性,并用定义证明你的判断;
(2)
,若不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/362bfce584209628bc4ad3f23e3d7b11.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/191e3c845e90f229f3c992aff85b92db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f9f7433193ef929c021485ad5e5dd25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
解题方法
3 . 已知函数
,
且
.
(1)若函数
的最小值为
,试证明:点
在定直线上;
(2)若
,
时,不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3afc15b3026f7116168150a4f53dcf3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c21aa63e98fb55e3fa436abf652c87e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1218eda19f74a1ed50ab106265c6621f.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba7204f43679af6935e494c59d40c6ff.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc2d3df37e73a8abea815f37dbb3fff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7dbb416ec1ff1984a724a4f48bf692.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6213c81ca727adbcdda8cbdbe10c30a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2023-12-15更新
|
178次组卷
|
2卷引用:四川省成都市石室中学2023-2024学年高三上学期期中考试理科数学试卷
解题方法
4 . 已知函数
的定义域为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7b7b68a326dd30b2f01c750a11dd6b9.png)
(1)用单调性的定义证明
在
上是增函数;
(2)若函数
是R上的减函数,且不等式
在
上恒成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aae57f61d1f0cb5dabb40e0a3720c21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7b7b68a326dd30b2f01c750a11dd6b9.png)
(1)用单调性的定义证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d479a86a1711709b2d100fe4daf3e7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8fe868d4152f599a9ae5a0dae150cb0.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5946299ed8f8c741a82c8d920e1e206.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ca9c06bb540e289c131ecfcf4d96952.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11b481c660bea0673fdd7b31679cab53.png)
您最近一年使用:0次
名校
解题方法
5 . 已知函数
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/24/caf4e040-c408-42a7-b3e8-144d109b4a90.png?resizew=194)
(1)判断函数的奇偶性,并利用定义证明;
(2)判断函数
单调性(不需要证明),并画出
的图像.
(3)若不等式
在区间
上恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c47b2d73a4858fe5a169a0964c7e878e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/24/caf4e040-c408-42a7-b3e8-144d109b4a90.png?resizew=194)
(1)判断函数的奇偶性,并利用定义证明;
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2bed605a16f9afd9b63861e02056a3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73f0a7f52eb82472cce50381cbed1c16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
解题方法
6 . 设
,
.
(1)判断
的奇偶性,并证明;
(2)写出
的单调区间(直接写出结果);
(3)若当
时,函数
的图象恒在函数
的上方,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f70345d77b92867c548f44deae4891e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e3f0e295cc6fa40b8aaad1049e1f01f.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c735550bf19096ef02e7cc05b40a0879.png)
(3)若当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8408a1b2a46ac429c5398500b6223f3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f466a93c9e7acd29a0b5790668124f4a.png)
您最近一年使用:0次
2024-01-06更新
|
431次组卷
|
3卷引用:吉林省白山市2023-2024学年高一上学期期末教学质量监测数学试卷
吉林省白山市2023-2024学年高一上学期期末教学质量监测数学试卷江西省上饶市广丰区私立康桥中学2023-2024学年高一上学期期末模拟数学试题(已下线)高一数学开学摸底考 01-人教B版2019必修第一册+第二册摸底考试卷
名校
解题方法
7 . 设
,已知函数
.
(1)当
时,用定义证明
是
上的严格增函数;
(2)若定义在
上的奇函数
满足当
时,
,求
在区间
上的反函数
;
(3)对于(2)中的
,若关于
的不等式
在
上恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2476c8c0ae7946c94c3f2e401677e7f4.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b2798c6a26d02c5d2c8b1355c8c30.png)
(2)若定义在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ead3fdcb8fe8f5eb3dbe7d96cabc28b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/966d9dd819cba29980da3700422c2497.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d1a94ea3c278c2197572cc1b7725b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1a1c92c42188e3b2cb800d1186eab12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
(3)对于(2)中的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/352fdc419e6b6b9eb5bfc24dde2eb965.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb87c830a03204a5b783ad4c2ba49c4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2023-12-06更新
|
146次组卷
|
6卷引用:江苏省南京市第二十九中学2022-2023学年高一下学期2月期初考试数学试题
江苏省南京市第二十九中学2022-2023学年高一下学期2月期初考试数学试题江西省遂川中学2022-2023学年高一上学期期末考试数学试题(已下线)5.4 反函数-数学同步精品课堂(沪教版2020必修第一册)(已下线)单元高难问题03函数恒成立问题和存在性问题-【倍速学习法】(沪教版2020必修第一册)(已下线)专题16反函数-【倍速学习法】(沪教版2020必修第一册)上海市复旦大学附属中学2021-2022学年高一上学期期末数学试题
解题方法
8 . 已知函数
.
(1)判断
的单调性,并用单调性的定义证明;
(2)当
时,
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a2dcf157c86244e221e997a9f3c04e7.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b9b81feb84ce1523ae97d5bff2c4072.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c980b1bbe703432a5a8d44ca0b16e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
名校
解题方法
9 . 定义在
上的函数
满足:对任意的
,都有
.
(1)求证:函数
是奇函数;
(2)若当
时,有
,求证:
在
上是减函数;
(3)在(2)的条件下,若
,
对所有
,
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/455ba3d3e46977fcbe5b71f8bb9df4be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c75a15990fdcf1de0a9ac9f475e3c92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18ce23d4f9f61a8b1f99d11f4cd2c1d6.png)
(1)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5efe66db991b562c73ffb16c1e585870.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/455ba3d3e46977fcbe5b71f8bb9df4be.png)
(3)在(2)的条件下,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1947266214c98cfdeea15425a47de17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0519eee9b07f424d5682622512611fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/679c9edadb198dae2983e88f9ee58beb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec25b9d7ca47b780a744c2ebbf31d925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2024-01-05更新
|
498次组卷
|
4卷引用:河南省郑州市河南省实验中学2023-2024学年高一上学期12月月考数学试题
名校
解题方法
10 . 已知函数
定义域为R,且对任意的x,
,都有
,且当
时,
,其中
.
(1)证明:
是奇函数;
(2)不等式
对所有的
均成立,求实数m的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32447060a910faf370a7715ecf4c97e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/104fc7daa1aaefd69764e2616109a4c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebfdecc7f8089cb23c20d0a93ee1b601.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a64337ab40bd006e29941ca6c4e2e26.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6eeaa11e3c6071c43d2a9b715fce841.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/660db908fb9ba66444eec020d9c96faf.png)
您最近一年使用:0次