【题文】已知函数满足,且,若对任意的,总有成立,则在内的可能值有( )个.A.4B.3C.2D.1
题型:难度:来源:
【题文】已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327051500-94465.png)
满足
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327051501-90415.png)
,且
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327051501-49094.png)
,若对任意的
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327051502-78213.png)
,
总有
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327051502-30562.png)
成立,则
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327051503-25232.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327051503-18466.png)
内的可能值有( )个.
答案
【答案】C
解析
【解析】解:因为函数f(x)满足f(1)=a,且
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327051501-49094.png)
,若对任意的
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327051502-78213.png)
,总有f(n+3)=f(n)成立,则 说明是周期为3的函数,那么可知a在
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327051503-18466.png)
内的可能值有2,选C
举一反三
【题文】已知偶函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327051442-34395.png)
满足条件:当
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327051443-66315.png)
时,恒有
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327051443-35260.png)
,且
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327051443-48390.png)
时,有
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327051443-20192.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327051444-85057.png)
的大小关系是 ( )
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327051444-99585.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327051445-72452.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327051445-92801.png)
【题文】已知偶函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327051422-31234.png)
满足条件:当
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327051422-86338.png)
时,恒有
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327051422-36445.png)
,且
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327051422-26112.png)
时,有
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327051422-27560.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327051423-59220.png)
的大小关系是 ( )
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327051423-78999.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327051424-25125.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327051424-82211.png)
【题文】:已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327051401-69875.png)
是定义在R上的最小正周期为3的奇函数,当
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327051401-30892.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327051401-78698.png)
,则
。
【题文】:已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327051353-93784.png)
是定义在R上的最小正周期为3的奇函数,当
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327051353-33727.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327051354-83076.png)
,则
。
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