【题文】(本题12分)已知全集,,,求集合及.
题型:难度:来源:
答案
【答案】
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322145536-22576.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322145536-33861.png)
.
解析
【解析】
试题分析:先用列举法表示全集
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322145536-19357.png)
和集合
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322145537-49803.png)
,然后根据集合的运算求出
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322145536-38559.png)
和
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322145537-53141.png)
,最后求出
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322145536-97268.png)
.此类题目重在考查集合与集合的并、交、补运算,关键在于明确构成所给的各个集合的元素,必要时可借助数轴,进而准确的求解.
试题解析:由题知
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322145537-65095.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322145537-12394.png)
, 2分
∵
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322145535-66066.png)
,∴
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322145536-38559.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322145537-24782.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322145538-96299.png)
, 6分
∴
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322145538-82816.png)
8分
∴
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322145538-97897.png)
. 12分
考点:集合的表示及运算.
举一反三
【题文】(本题12分)若集合
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322145414-51239.png)
,集合
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322145414-79740.png)
,且
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322145414-41228.png)
,求实数
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322145415-50622.png)
的取值范围.
【题文】(本题13分)已知集合
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322145343-93992.png)
函数
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322145344-24472.png)
的定义域为集合B.
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322145344-81672.png)
,求实数
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322145344-16070.png)
的值;
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322145345-79740.png)
,求实数
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322145344-16070.png)
的取值范围.
【题文】(本题14分)对于函数
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322145320-25973.png)
,若
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322145320-29554.png)
,则称
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322145320-46241.png)
为
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322145320-25973.png)
的“不动点”,若
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322145320-21765.png)
,则称
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322145320-46241.png)
为
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322145320-25973.png)
的“稳定点”,函数
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322145320-25973.png)
的“不动点”和“稳定点”的集合分别记为A和B,即
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322145321-63040.png)
.
(1)设
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322145321-76820.png)
,求集合A和B;
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322145321-64963.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322145321-27259.png)
,求实数
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322145322-16978.png)
的取值范围;
(3)若
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322145322-13434.png)
,求证:
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322145322-15210.png)
.
【题文】已知集合
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322145214-52005.png)
,那么
![](http://img.shitiku.com.cn/uploads/allimg/20200322/20200322145214-84455.png)
子集的个数是:( )
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