题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083114-41850.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083115-11375.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083115-31115.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083115-22658.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083115-66406.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083114-41850.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083115-11375.png)
现给出下列命题:
① 函数
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083115-32309.png)
② 函数
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083115-70958.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083115-61944.png)
③ 如果定义域为
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083116-48382.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083116-17304.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083116-48382.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083116-39677.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083116-39677.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083116-20044.png)
④ 函数
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083117-24352.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083117-20036.png)
其中真命题的个数为
A.0 | B.1 | C.2 | D.3 |
答案
解析
试题分析:首先理解“高调函数”的定义:函数
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083114-41850.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083115-11375.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083115-31115.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083115-22658.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083115-66406.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083114-41850.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083115-11375.png)
据此研究四个函数:
对于①,即f(x)=(
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083117-94388.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083117-94388.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083117-94388.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083117-94388.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083115-32309.png)
对于②,f(x+1))=sin2(x+1)≥sin2x=f(x),当l=π时恒成立;所以函数f(x)=sin2x为R上的π高调函数,
所以②对;
对于③,f(x+m)=(x+m)2,f(x)=x2,令(x+m)2≥x2,即2mx+m2≥0在
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083116-48382.png)
∴m>0且2m(-1)+m2≥0,解得m≥2,故③对;
对于④ 函数
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083117-24352.png)
则由
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083117-49386.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083117-24352.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083117-20036.png)
得
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083118-13420.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083117-20036.png)
故正确的命题个数是3个,
故选D。
点评:新定义问题,具有较强的综合性。关键是阅读理解新定义内容,应用知识分析解决问题,利用数形结合的方法,应用图象解决问题,属中档题
核心考点
试题【设函数的定义域为D,若存在非零实数使得对于任意,有,且,则称为M上的高调函数. 现给出下列命题:① 函数为R上的1高调函数;② 函数为R上的高调函数;③ 如果定】;主要考察你对四种命题等知识点的理解。[详细]
举一反三
A.若![]() ![]() | B.若![]() ![]() |
C.若![]() ![]() | D.若![]() ![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083055-99601.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083055-79156.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083055-45393.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083055-72111.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083056-10440.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083056-91402.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083056-35201.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083056-22806.png)
A.(![]() ![]() ![]() | B.(![]() ![]() ![]() |
C.(![]() ![]() | D.![]() |
(1)方程
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083046-62557.png)
(2)动点到两个定点的距离之和为定长,则动点的轨迹为椭圆;
(3)动点
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083046-55404.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083046-80301.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083046-96616.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083046-81306.png)
(4)若双曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083046-78868.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083047-38549.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083047-31770.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083047-74427.png)
①双曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083034-71676.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083035-60787.png)
②在平面内, 设
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083035-57116.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083035-11058.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083035-43611.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083036-34872.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083036-85140.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083035-43611.png)
③方程
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083036-47874.png)
④过双曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083036-68776.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083036-48766.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083037-15502.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083037-62485.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083037-36027.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191102/20191102083037-15502.png)
其中真命题的序号为 (写出所有真命题的序号).
A.所有实数的平方都不是正数 | B.有的实数的平方是正数 |
C.至少有一个实数的平方是正数 | D.至少有一个实数的平方不是正数 |
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