【题文】已知函数是上的奇函数,且的图象关于直线对称,当时,,则 &
【题文】已知函数是上的奇函数,且的图象关于直线对称,当时,,则 &
题型:难度:来源:
【题文】已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032522-22849.png)
是
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032522-61691.png)
上的奇函数,且
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032522-22849.png)
的图象关于直线
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032522-48035.png)
对称,当
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032523-63601.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032523-74744.png)
,则
答案
【答案】1.
解析
【解析】由题意,得
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032523-18572.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032524-79971.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032524-84059.png)
,
即函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032522-22849.png)
是周期函数,且周期为4;则
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032524-89780.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032525-58257.png)
,
所以
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032525-34071.png)
考点:函数的奇偶性与周期性.
举一反三
【题文】已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032517-17748.png)
是
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032517-41501.png)
上的奇函数,且
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032517-17748.png)
的图象关于直线
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032517-20171.png)
对称,当
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032518-93350.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032518-81023.png)
,则
【题文】若
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032504-95042.png)
是
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032504-43329.png)
上周期为5的奇函数,且满足
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032504-96453.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032505-42647.png)
的值为
A.![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032506-43218.png) | B.1 | C.![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032506-51723.png) | D.2 |
【题文】已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032412-97110.png)
是
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032413-21371.png)
上的奇函数,且
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032412-97110.png)
的图象关于直线
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032413-60603.png)
对称,当
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032413-59795.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032413-16860.png)
,则
【题文】已知函数y=f(x)对于任意x∈R有
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032347-68635.png)
,且当x∈[-1,1]时,
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032347-18189.png)
,则以下命题正确的是:
①函数数y=f(x)是周期为2的偶函数;
②函数y=f(x)在[2,3]上单调递增;
③函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032348-76186.png)
的最大值是4;
④若关于x的方程
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032348-72395.png)
有实根,则实数m的范围是[0,2];
⑤当
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032348-73186.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032348-88398.png)
.
其中真命题的序号是_
_ __
【题文】若函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032330-81805.png)
的图像关于原点对称,则
.
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