【题文】设是定义在上的奇函数,且的图象关于直线对称,则
【题文】设是定义在上的奇函数,且的图象关于直线对称,则
题型:难度:来源:
【题文】设
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032157-17180.png)
是定义在
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032157-97972.png)
上的奇函数,且
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032158-46397.png)
的图象关于直线
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032158-11122.png)
对称,则
.
答案
【答案】
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032159-67999.png)
.
解析
【解析】
试题分析:∵
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032157-17180.png)
是定义在
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032157-97972.png)
上的奇函数,∴
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032200-62912.png)
,又∵
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032157-17180.png)
的图象关于直线
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032158-11122.png)
对称,
∴
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032200-56728.png)
,在
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032200-80764.png)
中,令
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032200-45811.png)
,
∴
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032201-20219.png)
,∴
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032201-92747.png)
,∴
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032201-35001.png)
.
考点:奇函数的性质.
举一反三
【题文】设偶函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032121-43011.png)
对任意
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032121-99538.png)
都有
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032122-32473.png)
,且当
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032122-93402.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032122-98732.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032123-98062.png)
( )
A.10 | B.![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032123-32653.png) | C.-10 | D.![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032123-36834.png) |
【题文】已知函数:①
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032047-29030.png)
,②
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032047-76638.png)
,③
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032047-13341.png)
.则以下四个命题对以上的三个函数都成立的是( )
命题
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032047-16272.png)
:
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032048-43610.png)
是奇函数;
命题
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032048-53638.png)
:
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032049-25897.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032049-16706.png)
上是增函数;
命题
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032049-64055.png)
:
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032050-32719.png)
;
命题
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032050-37846.png)
:
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032050-92173.png)
的图像关于直线
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032051-19197.png)
对称
【题文】给出下列命题:
①已知集合M满足
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032035-49812.png)
,且M中至多有一个偶数,这样的集合M有6个;
②函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032036-38908.png)
,在区间
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032036-55593.png)
上为减函数,则
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032036-47441.png)
的取值范围为
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032037-90262.png)
;
③已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032037-55612.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032037-68092.png)
;
④如果函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032038-84650.png)
的图象关于y轴对称,且
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032039-54075.png)
,
则当
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032039-54349.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032039-51274.png)
;
其中正确的命题的序号是
。
【题文】已知
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032001-70254.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032002-61645.png)
上是奇函数,且满足
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032002-74342.png)
,当
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032002-36379.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032002-81936.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327032003-22119.png)
的值为 ( )
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