名校
1 . 已知集合
是满足下列条件的函数
的全体:在定义域内存在实数
,使得
成立.
(1)判断幂函数
是否属于集合
?并说明理由;
(2)设
,
,
i)当
时,若
,求
的取值范围;
ii)若对任意的
,都有
,求
的取值范围
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1c8e4eb142751bf3e35b5c419115e52.png)
(1)判断幂函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a8756b76b2fb3289cb0f5a38623d5e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e80374f06a59d67e1235bd120d3baa39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16534214250c59605aae906eef0094c9.png)
i)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f12ce5fc6401ba953229e4388f229b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
ii)若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4d9b1cca22323ced9b4ff504244cf32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f12ce5fc6401ba953229e4388f229b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
您最近一年使用:0次
2017-12-22更新
|
595次组卷
|
6卷引用:广东省汕头市金山中学2018-2019学年高一下学期第一次月考数学试题
广东省汕头市金山中学2018-2019学年高一下学期第一次月考数学试题四川省石室中学2017-2018学年高一上学期半期考试数学试题1四川省石室中学2017-2018学年高一上学期半期考试数学试题2【全国百强校】江苏省南通市海安高级中学2018-2019学年高一上学期期中考试数学试题云南省大理下关一中教育集团2020-2021学年高一下学期期中考试数学试题(已下线)4.3对数(专题强化卷)-2021-2022学年高一数学课堂精选(人教版A版2019必修第一册)
名校
2 . 已知二次函数
满足
(
),且
.
(1)求
的解析式;
(2)若关于
的方程
在区间
上有唯一实数根,求实数
的取值范围(注:相等的实数根算一个).
(3)函数
,试问是否存在实数
,使得对任意
,
都有
成立,若存在,求出实数
的取值范围,若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c811aac7882ab358d59ee0ee49a029d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e61c9a7ed0961f8977a21dab37aab396.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c269b5fc40b6985e1aad2be09d29c6fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/599e13f74bcd5268afea7a6c0928403a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84a7792b5cd171fcf307992254c8202e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/756f2cef86c1e3cfa8d5aa09717e4290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85262fdbbf6fb2557813b886884a6628.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2017-11-27更新
|
1748次组卷
|
3卷引用:广东省揭阳市第一中学2018-2019学年高一下学期期中数学试题
3 . 已知函数
,
,且
.
(1)证明函数
在区间
上是增函数;
(2)设函数
. 若区间[2,5]是
的一个单调区间,
且在该区间上
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf7590785d8ee40f3d7206d4aa819265.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b8c164755dc2d7cff80fb4c9cffc9be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df2817c52144d06555e98131b5e657c4.png)
(1)证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6d804ef44bfc64f824b0ccef71765e.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ad24b182074510c1952e5948a6f8230.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
且在该区间上
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eee31b9dffcd91ff2f5477410bc09f95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
解题方法
4 . 已知
,函数
.
(1)当
时,求函数
的单调区间;
(2)当
时,求函数
在
上的最小值.
![](https://img.xkw.com/dksih/QBM/2016/4/29/1572608365166592/1572608371556352/STEM/ae2d95f0e6ba40ab86642d3456106f9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f520cd6d17408bf4eeb8bb902f46ac.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eda48853e8bdb7e266370b4e0d5a258.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf105efd4cf5f580d0561e54d923e347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af21c55c0038bf249efd676e59a632a1.png)
您最近一年使用:0次