【题文】若函数,当时,那么正确的结论是( )A.B.C. 2-a<2c D.
【题文】若函数,当时,那么正确的结论是( )A.B.C. 2-a<2c D.
题型:难度:来源:
答案
【答案】D.
解析
【解析】
试题分析:
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325195729-97513.png)
在R上单调递增,且
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325195729-83059.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325195729-13981.png)
,所以排除选项A,B;
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325195729-46630.png)
的图像关于
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325195730-87843.png)
轴对称,且
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325195729-83059.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325195731-86899.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325195731-55712.png)
,且
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325195732-11907.png)
,即
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325195732-77559.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325195733-64059.png)
,所以排除选项C;若
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325195733-67639.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325195734-51281.png)
,即
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325195734-52618.png)
;若
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325195734-74490.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325195734-55943.png)
,即
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325195735-73973.png)
;故选D.
考点:指数函数的图像与性质.
举一反三
【题文】已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325195102-73276.png)
.构造函数
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325195102-23026.png)
,定义如下:当
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325195102-25308.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325195103-47113.png)
;当
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325195103-80684.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325195103-22113.png)
.那么
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325195102-23026.png)
( )
A.有最大值3,最小值-1 |
B.有最大值3,无最小值 |
C.有最大值 ,无最小值 |
D.有最大值 ,最小值![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325195104-26655.png) |
【题文】若函数
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325194908-78436.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325194908-59205.png)
上单调递减,则实数
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325194908-28842.png)
的取值范围是
.
【题文】已知定义在
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325194814-14960.png)
上的奇函数
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325194814-56473.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325194815-24956.png)
时满足
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325194815-12643.png)
,且
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325194815-38421.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325194816-81233.png)
恒成立,则实数
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325194816-80028.png)
的最大值是
.
【题文】已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325194638-67711.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325194638-36799.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325194639-40756.png)
.
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325194639-76006.png)
时,求函数
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325194640-36622.png)
的最小值;
(2)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325194640-36622.png)
的最小值为
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325194640-28716.png)
,令
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325194641-75422.png)
,求
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325194641-67309.png)
的取值范围.
【题文】下列函数中,在区间
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325194511-46647.png)
上为增函数的是
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