【题文】(10分)设集合至多有个一元素,求实数的取值范围.
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【题文】(10分)设集合
![](http://img.shitiku.com.cn/uploads/allimg/20200314/20200314033826-24210.png)
至多有个一元素,求实数
![](http://img.shitiku.com.cn/uploads/allimg/20200314/20200314033827-19661.png)
的取值范围.
答案
【答案】
![](http://img.shitiku.com.cn/uploads/allimg/20200314/20200314033827-35730.png)
或
![](http://img.shitiku.com.cn/uploads/allimg/20200314/20200314033827-23225.png)
.
解析
【解析】
试题分析:集合M至多一个元素,则M只有一个元素或为空集,当M为空集时,方程没有实数根,注意字母a的讨论;当M只有一个元素时,方程的根有且只有一个,此题容易漏掉
![](http://img.shitiku.com.cn/uploads/allimg/20200314/20200314033827-35730.png)
的情况.
试题解析:
若集合
![](http://img.shitiku.com.cn/uploads/allimg/20200314/20200314033828-56681.png)
至多有个一元素
则
![](http://img.shitiku.com.cn/uploads/allimg/20200314/20200314033828-75178.png)
只有一个元素或为空集
那么
![](http://img.shitiku.com.cn/uploads/allimg/20200314/20200314033827-35730.png)
或
![](http://img.shitiku.com.cn/uploads/allimg/20200314/20200314033828-95443.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20200314/20200314033827-35730.png)
或
![](http://img.shitiku.com.cn/uploads/allimg/20200314/20200314033827-23225.png)
.
考点:集合、元素的概念.
举一反三
【题文】满足M
![](http://img.shitiku.com.cn/uploads/allimg/20200314/20200314033621-39967.png)
{a
1, a
2, a
3},且M ∩{a
1 ,a
2, a
3}={a
3}的集合M的子集个数是 ( )
【题文】下列五个写法:①
![](http://img.shitiku.com.cn/uploads/allimg/20200314/20200314033552-23062.png)
;②
![](http://img.shitiku.com.cn/uploads/allimg/20200314/20200314033552-81946.png)
;③
![](http://img.shitiku.com.cn/uploads/allimg/20200314/20200314033553-69637.png)
④
![](http://img.shitiku.com.cn/uploads/allimg/20200314/20200314033553-98116.png)
;⑤
![](http://img.shitiku.com.cn/uploads/allimg/20200314/20200314033554-11951.png)
,其中正确的序号是_______________.
【题文】设集合A={-1,3,5},若
![](http://img.shitiku.com.cn/uploads/allimg/20200314/20200314033548-70005.png)
:
![](http://img.shitiku.com.cn/uploads/allimg/20200314/20200314033548-52903.png)
是集合A到集合B的映射,则集合B可以是( )
A.{0,2,3} | B.{1,2,3} | C.{-3,5} | D.{-3,5,9} |
【题文】下列叙述正确的是( )
A 方程
![](http://img.shitiku.com.cn/uploads/allimg/20200314/20200314033513-44167.png)
的根构成的集合为
![](http://img.shitiku.com.cn/uploads/allimg/20200314/20200314033513-90805.png)
B.
![](http://img.shitiku.com.cn/uploads/allimg/20200314/20200314033513-22618.png)
C.集合
![](http://img.shitiku.com.cn/uploads/allimg/20200314/20200314033514-45391.png)
表示的集合是
![](http://img.shitiku.com.cn/uploads/allimg/20200314/20200314033514-22975.png)
D.集合
![](http://img.shitiku.com.cn/uploads/allimg/20200314/20200314033514-97992.png)
与集合
![](http://img.shitiku.com.cn/uploads/allimg/20200314/20200314033515-19224.png)
是不同的集合
【题文】定义集合运算:
![](http://img.shitiku.com.cn/uploads/allimg/20200314/20200314033245-12523.png)
※
![](http://img.shitiku.com.cn/uploads/allimg/20200314/20200314033245-22869.png)
,设
![](http://img.shitiku.com.cn/uploads/allimg/20200314/20200314033245-39759.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200314/20200314033246-98311.png)
,则集合A※B的所有元素之和为( )
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