【题文】函数在上单调,则实数的取值范围是 ( )A.B.C.D.
题型:难度:来源:
答案
【答案】A
解析
【解析】本题考查分段函数的含义,分段函数的单调性,二次函数和指数函数的性质.
要使函数
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325095039-76776.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325095039-26731.png)
上单调,需使函数
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325095039-76776.png)
分别在
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325095040-96369.png)
和
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325095040-80229.png)
上的单调性一致,并且分段函数在分段
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325095040-64860.png)
处满足该单调性;
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325095040-84351.png)
时,函数
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325095040-42838.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325095040-96369.png)
上是增函数,要使函数
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325095040-74437.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325095041-99035.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325095039-26731.png)
上单调,需单调递增;则实数
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325095039-64953.png)
满足
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325095041-36965.png)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325095041-88810.png)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325095041-59853.png)
时,函数
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325095040-42838.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325095040-96369.png)
上是减函数,要使函数
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325095040-74437.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325095041-99035.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325095039-26731.png)
上单调,需单调递减;则实数
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325095039-64953.png)
满足
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325095041-54439.png)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325095042-46952.png)
综上:实数
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325095039-64953.png)
的取值范围是
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325095042-81583.png)
.故选A
举一反三
【题文】已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325094837-35180.gif)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325094837-81533.gif)
__
▲__;
【题文】已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325094828-66423.gif)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325094828-51435.gif)
__
▲__;
【题文】设函数
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325094822-43781.png)
,则函数
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325094822-93980.png)
的零点的个数为(▲)
【题文】设函数
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325094752-48886.png)
,则函数
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325094752-53198.png)
的零点的个数为(▲)
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