【题文】(每小题6分,共12分)求下列函数的定义域:(1) (2) .
题型:难度:来源:
【题文】(每小题6分,共12分)求下列函数的定义域:
(1)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324224449-66195.png)
.
答案
【答案】(1)
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324224450-96782.png)
;(2) {x| x
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324224450-13928.png)
2}
解析
【解析】(1)求函数的定义域就是使函数有意义的x的取值集合,本小题x应满足
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324224450-24687.png)
,据此可得到x的取值范围,从而得到函数的定义域.
(2)本小题应满足被开方数为非负数即
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324224450-17866.png)
,从而转化为指数不等式来解.
(1)
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324224451-44473.png)
,即定义域为
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324224450-96782.png)
;
(2)依题意得
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324224450-17866.png)
,
所以,
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324224451-27909.png)
,即
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324224451-32505.png)
所以,x
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324224450-13928.png)
2
所以,函数的定义域为{x| x
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324224450-13928.png)
2}
举一反三
【题文】函数
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324224434-20599.png)
的定义域为( )
【题文】设一个函数的解析式为
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324224427-95872.png)
,它的值域为
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324224427-62476.png)
,则该函数的定义域为
.
【题文】有下列四个命题:
(1)函数
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324224409-53000.png)
为偶函数; (2)函数
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324224409-86223.png)
;
(3)已知集合
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324224410-11660.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324224410-21220.png)
,若
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324224410-19870.png)
,则实数
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324224410-43180.png)
的取值集合为
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324224411-80702.png)
; (4)集合
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324224411-86207.png)
,对应法则f:“求平方根”,则
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324224411-15427.png)
是A到B的映射;你认为正确命题的序号是
(把正确的序号都写上).
【题文】函数
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324224401-33458.png)
的定义域为
【题文】函数
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324224356-31943.png)
的定义域是
![](http://img.shitiku.com.cn/uploads/allimg/20200324/20200324224357-72072.png)
,则其值域是 ( )
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