【题文】若函数在区间上是单调增函数,则常数的取值范围是 .
题型:难度:来源:
【题文】若函数
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095848-23280.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095848-64736.png)
在区间
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095849-10238.png)
上是单调增函数,则常数
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095849-24300.png)
的取值范围是
.
答案
【答案】
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095849-84438.png)
解析
【解析】
试题分析:本题考查复合函数的单调性,设
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095850-10469.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095850-93024.png)
(
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095850-28463.png)
)
当
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095851-29726.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095850-10469.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095851-25754.png)
上为减函数,
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095850-93024.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095851-15679.png)
上为减函数,
则
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095851-73720.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095851-15679.png)
上为增函数,因为函数
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095848-23280.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095848-64736.png)
在区间
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095849-10238.png)
上是
单调增函数,所以要求
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095851-48494.png)
,又
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095851-29726.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095849-84438.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095852-88750.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095850-10469.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095851-25754.png)
上为增函数,
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095850-93024.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095851-15679.png)
上为减函数,
则
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095851-73720.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095851-15679.png)
上为减函数,不合题意;
考点:1.对数函数图象和性质;2.复合函数的单调性“同增异减”;
举一反三
【题文】(本小题满分12分)
(1)化简
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095838-19876.png)
log
85
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095839-51483.png)
log
2516 + log
324 .
(2)若log
2(3x-2)<2,试求x的取值范围.
【题文】(本小题满分12分)
(1)化简
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095831-59685.png)
log
85
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095831-53159.png)
log
2516 + log
324 .
(2)若log
2(3x-2)<2,试求x的取值范围.
【题文】(本题满分14分)
(1)已知
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095820-23620.png)
,求
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095820-39418.png)
的值;
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095820-12135.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095821-88473.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095821-26831.png)
,且
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095821-95211.png)
,求
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095821-88473.png)
的值.
【题文】(本题满分14分)
(1)已知
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095800-85946.png)
,求
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095801-24408.png)
的值;
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095801-98218.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095801-14306.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095802-53609.png)
,且
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095802-92437.png)
,求
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095801-14306.png)
的值.
【题文】已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095750-50665.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095750-58817.png)
的值为( )
A.![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095751-24285.png) | B.4 | C.2 | D.![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330095751-53314.png) |
最新试题
热门考点