【题文】函数=的定义域为,集合=,(1)求:集合; (2)若,求的取值范围.
题型:难度:来源:
【题文】函数
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324205359-60673.png)
=
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324205359-91244.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324205400-42448.png)
的定义域为
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324205400-96879.png)
,集合
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324205400-55271.png)
=
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324205401-66647.png)
,
(1)求:集合
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324205400-96879.png)
; (2)若
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324205401-23350.png)
,求
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324205401-11719.png)
的取值范围.
答案
【答案】(1)
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324205402-37685.png)
;(2)
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324205402-74559.png)
.
解析
【解析】
试题分析:(1)要使函数
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324205359-60673.png)
有意义,只需满足
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324205402-87416.png)
,从而求出集合
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324205400-96879.png)
;(2)由(1)可得集合
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324205402-37685.png)
,而集合
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324205403-21473.png)
,若
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324205403-13521.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324205403-92792.png)
,所以
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324205404-41461.png)
.
试题解析:(1)要使函数
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324205359-60673.png)
有意义,只需满足
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324205402-87416.png)
,解得
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324205404-21754.png)
,即
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324205404-53172.png)
,从而求出集合
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324205402-37685.png)
.
(2)由(1)可得集合
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324205402-37685.png)
,而集合
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324205403-21473.png)
,若
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324205403-13521.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324205403-92792.png)
,所以
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324205404-41461.png)
,即
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324205401-11719.png)
的取值范围是
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324205402-74559.png)
.
考点:本题主要考查了函数的定义域的定义,集合间的基本关系和基本运算.
举一反三
【题文】已知集合
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324205335-58537.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324205335-91264.png)
( )
【题文】函数
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324205328-33628.png)
的定义域为____________.
【题文】函数
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324205317-18466.png)
的定义域是( )
【题文】已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324205311-78174.png)
的定义域为
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324205311-40461.png)
,函数
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324205311-31125.png)
的定义域为
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324205312-12470.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324205312-39620.png)
( )
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