【题文】若是的最小值,则的取值范围为( ).A.[-1,2]B.[-1,0]C.[1,2]D.
【题文】若是的最小值,则的取值范围为( ).A.[-1,2]B.[-1,0]C.[1,2]D.
题型:难度:来源:
【题文】
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325031955-79119.png)
若
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325031956-34990.png)
是
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325031956-49861.png)
的最小值,则
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325031956-84144.png)
的取值范围为( ).
A.[-1,2] | B.[-1,0] | C.[1,2] | D.![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325031957-92609.png) |
答案
【答案】D
解析
【解析】由于当
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325031957-34017.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325031957-58483.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325031958-22170.png)
时取得最小值
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325031958-91448.png)
,由题意当
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325031958-72793.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325031959-72759.png)
应该是递减的,则
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325031959-42751.png)
,此时最小值为
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325031959-74315.png)
,因此
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325031959-38323.png)
,解得
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325032000-89675.png)
,选D.
【考点】分段函数的单调性与最值问题.
举一反三
【题文】设
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325031944-48821.png)
是定义在R上的周期为2的函数,当
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325031945-68569.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325031945-31106.png)
,则
.
【题文】已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325031924-11862.png)
,若
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325031924-92069.png)
,则a=( )
A.![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325031925-32166.png) | B.![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325031925-25952.png) | C.1 | D.2 |
【题文】设
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325031902-32945.png)
是定义在R上的周期为2的函数,当
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325031902-11978.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325031903-80492.png)
,
则
.
【题文】设函数
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325031838-24576.png)
,若对任意给定的
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325031838-50302.png)
,都存在唯一的
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325031838-35881.png)
,满足
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325031839-58856.png)
,则正实数
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325031839-77747.png)
的最小值是
.
【题文】已知实数
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325031823-93761.png)
,函数
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325031824-65770.png)
若
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325031824-50076.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325031825-95659.png)
的值为________.
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