【题文】设,则使函数的定义域为且是奇函数的所有值为 (
【题文】设,则使函数的定义域为且是奇函数的所有值为 (
题型:难度:来源:
【题文】设
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325005114-10189.png)
,则使函数
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325005114-99950.png)
的定义域为
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325005114-55207.png)
且是奇函数的所有
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325005114-11521.png)
值为 ( )
A.-1,3 | B.-1,1 | C.1,3 | D.-1,1,3 |
答案
【答案】C
解析
【解析】分析:分别验证
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325005115-41783.png)
=-1,1,
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325005115-65805.png)
,3知当
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325005115-41783.png)
=1或
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325005115-41783.png)
=3时,函数y=
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325005115-95325.png)
的定义域是R且为奇函数.
解:当
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325005115-41783.png)
=-1时,y=x
-1的定义域是x|x≠0,且为奇函数;
当
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325005115-41783.png)
=1时,函数y=x的定义域是R且为奇函数;
当
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325005115-41783.png)
=
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325005115-65805.png)
时,函数y=
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325005116-83229.png)
的定义域是
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325005116-29240.png)
且为非奇非偶函数.
当
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325005115-41783.png)
=3时,函数y=x的定义域是R且为奇函数.
故选C.
举一反三
【题文】设
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325005103-88273.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325005103-60466.png)
的定义域为 ( )
【题文】函数
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325005100-63695.gif)
的定义域为_________________
【题文】函数
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325005056-40876.gif)
的定义域
[
【题文】已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325005050-76784.gif)
的定义域为
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325005050-81327.gif)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325005050-14973.gif)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325005051-53370.gif)
的取值范围是 ;
【题文】设函数
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325005045-32638.gif)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325005045-20560.gif)
=" " ▲ .
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