【题文】奇函数满足对任意都有成立,且,则的值为( )A.B.C.D.
【题文】奇函数满足对任意都有成立,且,则的值为( )A.B.C.D.
题型:难度:来源:
【题文】奇函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327042551-71046.png)
满足对任意
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327042551-52234.png)
都有
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327042551-91842.png)
成立,且
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327042551-73425.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327042551-95868.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327042552-22005.png)
的值为( )
答案
【答案】D
解析
【解析】
试题分析:
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327042553-43711.png)
是
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327042553-19900.png)
上的奇函数,则
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327042553-77052.png)
,且
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327042551-91842.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327042553-12820.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327042554-64487.png)
,故函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327042554-85584.png)
的一个周期为
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327042552-97571.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327042554-12582.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327042554-80058.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327042555-85225.png)
,
所以
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327042555-23731.png)
,选D.
考点:1.函数的周期性;2.函数的奇偶性
举一反三
【题文】已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327042528-28009.png)
是定义在
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327042528-36303.png)
上的奇函数,且对于任意
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327042529-78253.png)
,恒有
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327042529-53314.png)
成立,当
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327042529-92803.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327042530-17236.png)
,则
.
【题文】已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327042514-12883.png)
是定义在
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327042514-18767.png)
上的奇函数,且对于任意
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327042515-18958.png)
,恒有
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327042515-14741.png)
成立,当
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327042515-74869.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327042516-29487.png)
,则
.
【题文】下列函数中,最小正周期为
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327042504-32691.png)
的偶函数为( )
【题文】下列函数中,最小正周期为
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327042450-71721.png)
的偶函数为( )
【题文】若函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327042425-49932.png)
的图象经过点
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327042425-74095.png)
,则函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327042425-23020.png)
的图象必定经过的点的坐标
是
.
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