【题文】已知集合,,,且,求的取值范围.
【题文】已知集合,,,且,求的取值范围.
题型:难度:来源:
答案
【答案】
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322164549-91930.png)
.
解析
【解析】
试题分析:从条件的描述,可以将问题等价于,求
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322164549-50977.png)
的范围,使当
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322164550-47771.png)
时,函数
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322164550-68021.png)
的值域是函数
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322164550-83717.png)
的子集,
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322164550-57340.png)
的值域易得,即为
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322164551-85969.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322164551-97702.png)
的值域要根据
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322164549-50977.png)
的具体取值范围分类讨论才可求得,从而可以建立关于
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322164549-50977.png)
的不等式,可求得
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322164549-50977.png)
的取值范围是
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322164549-91930.png)
.
试题解析:
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322164551-64257.png)
,当
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322164551-95255.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322164551-72129.png)
,
而
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322164549-54902.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322164552-37433.png)
这是矛盾的;
当
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322164552-28795.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322164552-28928.png)
,而
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322164549-54902.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322164552-21021.png)
;
当
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322164553-74625.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322164553-17784.png)
,而
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322164549-54902.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322164553-99685.png)
;
∴
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322164549-91930.png)
.
考点:1.函数的值域;2.集合的关系.
举一反三
【题文】 如图中阴影部分表示的集合是( )
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322164506-66011.png)
【题文】已知
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322164440-56361.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322164440-79515.png)
( )
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