真题
名校
1 . 对定义域
的函数
,
,规定:
函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa65bd65401e3ba6873eb7b8115cf2a7.png)
(1)若函数
,
,写出函数
的解析式;
(2)求问题(1)中函数
的值域;
(3)若
,其中
是常数,且
,请设计一个定义域为R的函
数
,及一个
的值,使得
,并予以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0606be557187bb410105f7c9e7df32b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa65bd65401e3ba6873eb7b8115cf2a7.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ec5c8dcdeb8d4250a258a2f9fee0948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0c4473159277aed64ea96c4af087954.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
(2)求问题(1)中函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/810a58271edb9c987cb9f8bcb562c70c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d204082daeea4b4a5b8396ebf2b80e9e.png)
数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/520521462cf21c660b7a28a7d39448fb.png)
您最近一年使用:0次
2016-12-04更新
|
1220次组卷
|
9卷引用:2005年普通高等学校招生考试数学(理)试题(上海卷)
2005年普通高等学校招生考试数学(理)试题(上海卷)上海市交通大学附属中学2017-2018学年高一下学期开学考试数学试题沪教版(上海) 高三年级 新高考辅导与训练 第一章 集合与函数 三、指数函数与对数函数(已下线)课时12 函数的概念、函数关系及运算-2022年高考数学一轮复习小题多维练(上海专用)湖南省常德市石门县一中2017届高三上学期8月单元测理科数学试题广西南宁市第三中学2019-2020学年高一下学期期末考试数学试题广西南宁三中2019-2020学年高一(下)期末数学试题沪教版(2020) 一轮复习 堂堂清 第三单元 3.4 二倍角及半角的三角公式(已下线)专题02 函数的综合应用-1
真题
2 . f(x)=x+
的定义域为(0,+∞),且f(2)=2+
.设点P是函数图象上的任意一点,过点P分别作直线y=x和y轴的垂线,垂足分别为M、N.
(1)求a的值.
(2)问:|PM|•|PN|是否为定值?若是,则求出该定值;若不是,请说明理由.
(3)设O为坐标原点,求四边形OMPN面积的最小值.
![](https://img.xkw.com/dksih/QBM/2014/6/10/1571762739322880/1571762744942592/STEM/5ac7d575a5084eb6946b2286fd6451a2.png)
![](https://img.xkw.com/dksih/QBM/2014/6/10/1571762739322880/1571762744942592/STEM/ade60f07751d4bbbb684606baa62e4a5.png)
(1)求a的值.
(2)问:|PM|•|PN|是否为定值?若是,则求出该定值;若不是,请说明理由.
(3)设O为坐标原点,求四边形OMPN面积的最小值.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/11/564eb46a-b20c-4755-9f08-d2edb9e23b92.png?resizew=224)
您最近一年使用:0次
真题
3 . 定义域为R,且对任意实数
都满足不等式
的所有函数
组成的集合记为M,例如,函数
.
(1)已知函数
,证明:![](https://img.xkw.com/dksih/QBM/2011/1/11/1569961689497600/1569961694953472/STEM/f005048aef5b4c00bfd04be65aea1a50.png?resizew=36)
;
(2)写出一个函数
,使得
,并说明理由;
(3)写出一个函数![](https://img.xkw.com/dksih/QBM/2011/1/11/1569961689497600/1569961694953472/STEM/f005048aef5b4c00bfd04be65aea1a50.png?resizew=36)
,使得数列极限
![](https://img.xkw.com/dksih/QBM/2011/1/11/1569961689497600/1569961694953472/STEM/5274506c4be74f0382ffb8c9c3adb8ce.png?resizew=37)
![](https://img.xkw.com/dksih/QBM/2011/1/11/1569961689497600/1569961694953472/STEM/016ed019eee54f78ad46ffa2f0de3662.png?resizew=183)
![](https://img.xkw.com/dksih/QBM/2011/1/11/1569961689497600/1569961694953472/STEM/f005048aef5b4c00bfd04be65aea1a50.png?resizew=36)
![](https://img.xkw.com/dksih/QBM/2011/1/11/1569961689497600/1569961694953472/STEM/d52958cc2d114b44942f70bb5084e671.png?resizew=123)
(1)已知函数
![](https://img.xkw.com/dksih/QBM/2011/1/11/1569961689497600/1569961694953472/STEM/fb8baade7cdb4d2b95b88a730759d893.png?resizew=120)
![](https://img.xkw.com/dksih/QBM/2011/1/11/1569961689497600/1569961694953472/STEM/f005048aef5b4c00bfd04be65aea1a50.png?resizew=36)
![](https://img.xkw.com/dksih/QBM/2011/1/11/1569961689497600/1569961694953472/STEM/1abe62282f8d4473a2d68380e985fff9.png?resizew=33)
(2)写出一个函数
![](https://img.xkw.com/dksih/QBM/2011/1/11/1569961689497600/1569961694953472/STEM/f005048aef5b4c00bfd04be65aea1a50.png?resizew=36)
![](https://img.xkw.com/dksih/QBM/2011/1/11/1569961689497600/1569961694953472/STEM/0eec3ffa469c462d8d623a1c84694233.png?resizew=68)
(3)写出一个函数
![](https://img.xkw.com/dksih/QBM/2011/1/11/1569961689497600/1569961694953472/STEM/f005048aef5b4c00bfd04be65aea1a50.png?resizew=36)
![](https://img.xkw.com/dksih/QBM/2011/1/11/1569961689497600/1569961694953472/STEM/1abe62282f8d4473a2d68380e985fff9.png?resizew=33)
![](https://img.xkw.com/dksih/QBM/2011/1/11/1569961689497600/1569961694953472/STEM/1788617445624ded8170a9ac3b8e4e78.png?resizew=183)
您最近一年使用:0次
4 . 将函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99ddb41cb7db4d074615b7ab52138017.png)
的图像绕坐标原点逆时针方向旋转角![](https://img.xkw.com/dksih/QBM/2010/3/5/1569628003540992/1569628141158400/STEM/65f7582be5114a98b6f7239e611e6524.png?resizew=14)
,得到曲线
.若对于每一个旋转角
,曲线
都是一个函数的图像,则
的最大值为__________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99ddb41cb7db4d074615b7ab52138017.png)
![](https://img.xkw.com/dksih/QBM/2010/3/5/1569628003540992/1569628141158400/STEM/31839821393b43cd9e5d3d94e01df841.png?resizew=68)
![](https://img.xkw.com/dksih/QBM/2010/3/5/1569628003540992/1569628141158400/STEM/65f7582be5114a98b6f7239e611e6524.png?resizew=14)
![](https://img.xkw.com/dksih/QBM/2010/3/5/1569628003540992/1569628141158400/STEM/1900ff93a6044d869ff990f1ace2de92.png?resizew=78)
![](https://img.xkw.com/dksih/QBM/2010/3/5/1569628003540992/1569628141158400/STEM/ea7cbc5a366144ca9ffa6e37646978f9.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2010/3/5/1569628003540992/1569628141158400/STEM/65f7582be5114a98b6f7239e611e6524.png?resizew=14)
![](https://img.xkw.com/dksih/QBM/2010/3/5/1569628003540992/1569628141158400/STEM/ea7cbc5a366144ca9ffa6e37646978f9.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2010/3/5/1569628003540992/1569628141158400/STEM/f4daa6a0c8714cb8b09c8430664d254d.png?resizew=16)
您最近一年使用:0次
2016-11-30更新
|
2051次组卷
|
3卷引用:2009年普通高等学校招生全国统一考试理科数学(上海卷)