题目内容
已知A={x||x-a|<4},B={x|
}.
(1)若a=1,求
;
(2)若
R,求实数a的取值范围.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823224704015528.png)
(1)若a=1,求
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823224704031448.png)
(2)若
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823224704047454.png)
解:(1) a=1时,A=
=![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823224704109699.png)
B=![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823224704140775.png)
∴A∩B=
---------6分
(2)∵
B=![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823224704140775.png)
且
R
∴
解得:![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823224704281432.png)
∴实数a的取值范围是
-------------12分
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823224704078688.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823224704109699.png)
B=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823224704140775.png)
∴A∩B=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823224704156911.png)
(2)∵
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823224704187864.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823224704140775.png)
且
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823224704249457.png)
∴
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823224704265789.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823224704281432.png)
∴实数a的取值范围是
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823224704312428.png)
本试题主要是考查了集合的交集和并集的运算的综合运用。
(1)因为a=1时,A=
=![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823224704109699.png)
B=![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823224704140775.png)
因此可知A∩B=
-
(2)∵
B=![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823224704140775.png)
且
R
∴
解得:![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823224704281432.png)
得到结论。
(1)因为a=1时,A=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823224704078688.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823224704109699.png)
B=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823224704140775.png)
因此可知A∩B=
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823224704156911.png)
(2)∵
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823224704187864.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823224704140775.png)
且
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823224704249457.png)
∴
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823224704265789.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823224704281432.png)
得到结论。
![](http://thumb.zyjl.cn/images/loading.gif)
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