题目内容
已知集合
,
,
(1)若
,求
.
(2)若
,求实数a的取值范围。
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225135331816.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225135347676.png)
(1)若
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225135471454.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225135487447.png)
(2)若
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225135503602.png)
解:(1)![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225135534762.png)
=
;
(2)
或![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225135612508.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225135534762.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225135549598.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225135549598.png)
(2)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225135596416.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225135612508.png)
本试题主要是考查了集合的交集的运算,以及集合间关系的运用。
(1)根据当
时,
,
,从而得到交集
(2)由于
,利用数轴法得到结论。
解:(1)当
时,
,![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225135674679.png)
=![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225135534762.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225135549598.png)
=![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225135549598.png)
(2)依题意:
或![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225136283524.png)
或![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225135612508.png)
即实数a的取值范围为
或![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225135612508.png)
(1)根据当
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225135471454.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225135659808.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225135674679.png)
(2)由于
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225135503602.png)
解:(1)当
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225135471454.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225135659808.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225135674679.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225136017468.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225135534762.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225135549598.png)
=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225135549598.png)
(2)依题意:
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225136220413.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225136283524.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225135596416.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225135612508.png)
即实数a的取值范围为
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225135596416.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823225135612508.png)
![](http://thumb.zyjl.cn/images/loading.gif)
练习册系列答案
相关题目