【题文】(21分).若非零函数对任意实数均有¦(a+b)=¦(a)·¦(b),且当时,. (1)求证:; &
【题文】(21分).若非零函数对任意实数均有¦(a+b)=¦(a)·¦(b),且当时,. (1)求证:; &
题型:难度:来源:
【题文】(21分).若非零函数
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325083653-51522.png)
对任意实数
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325083653-83843.png)
均有¦(a+b)=¦(a)·¦(b),且当
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325083653-33751.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325083654-99308.png)
.
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325083654-13771.png)
;
(2)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325083653-51522.png)
为减函数;
(3)当
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325083654-98752.png)
时,解不等式
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325083654-28697.png)
答案
【答案】解:(1)
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325083654-16310.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325083655-61026.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325083655-99825.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325083655-74272.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325083655-57130.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325083653-51522.png)
为减函数
(3)由
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325083656-25102.png)
原不等式转化为
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325083656-96869.png)
,结合(2)得:
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325083656-42519.png)
故不等式的解集为
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325083656-84235.png)
.
解析
【解析】略
举一反三
【题文】已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325083641-80284.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325083642-27512.png)
=
。
【题文】已知点
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325083631-41426.png)
的坐标
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325083631-29548.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325083631-68505.png)
满足
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325083632-57384.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325083632-41813.png)
的最大值是
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325083633-20712.png)
、
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325083633-81138.png)
、
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325083634-56499.png)
、
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325083634-62798.png)
、
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325083635-91346.png)
最新试题
热门考点