【题文】:己知是定义在R上的奇函数,当时,,那么不等式的解集是( )A.B.或C.D.或
【题文】:己知是定义在R上的奇函数,当时,,那么不等式的解集是( )A.B.或C.D.或
题型:难度:来源:
【题文】:己知
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327005114-59937.png)
是定义在R上的奇函数,当
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327005115-19891.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327005115-72866.png)
,那么不等式
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327005115-46499.png)
的解集是( )
答案
【答案】:B
解析
【解析】:本题考查函数的奇偶性.
当
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327005115-19891.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327005115-72866.png)
,而
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327005117-31565.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327005118-67388.png)
;所以
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327005118-12905.png)
;
又
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327005114-59937.png)
是定义在R上的奇函数,则
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327005119-60598.png)
;
所以
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327005119-97435.png)
,所以
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327005120-44034.png)
,即当
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327005117-31565.png)
时
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327005120-44034.png)
.
所以
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327005120-48348.png)
⑴当
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327005120-29556.png)
时,由
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327005115-46499.png)
得
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327005120-83670.png)
,解得
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327005121-89366.png)
;
⑵当
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327005121-22488.png)
时,由
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327005115-46499.png)
得
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327005121-10708.png)
,解得
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327005121-56156.png)
;
所以原不等式的解集为
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327005116-15271.png)
或
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327005116-75079.png)
故正确答案为B
举一反三
【题文】定义在r上的偶函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327004808-11947.jpg)
满足
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327004808-59986.jpg)
,当:
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327004808-11339.jpg)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327004809-78284.jpg)
,则
A
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327004809-92935.jpg)
B
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327004809-71393.jpg)
C
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327004809-14305.jpg)
D
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327004810-35501.jpg)
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