【题文】若函数且在区间内单调递增,则的取值范围是( )A.B.C.D.
【题文】若函数且在区间内单调递增,则的取值范围是( )A.B.C.D.
题型:难度:来源:
【题文】若函数
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102951-49534.png)
且
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102951-61336.png)
在区间
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102951-94384.png)
内单调递增,则
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102951-44196.png)
的取值范
围是( )
答案
【答案】B.
解析
【解析】
试题分析:由题意得:
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102953-63974.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102953-91831.png)
恒成立,即
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102953-51054.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102953-91831.png)
恒成立,∴
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102954-80358.png)
,若
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102954-55039.png)
:则
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102954-64376.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102953-91831.png)
上单调递减,即
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102955-99687.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102953-91831.png)
恒成立,
∴
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102955-54577.png)
;若
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102955-70397.png)
:则
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102956-90688.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102953-91831.png)
上单调递增,且恒为正,即
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102956-35152.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102953-91831.png)
恒成立,这与
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102955-70397.png)
矛盾,综上,实数
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102951-44196.png)
的取值范围是
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102952-86984.png)
.
考点:1.对数函数的单调性;2.恒成立问题.
举一反三
【题文】对于函数
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102930-60001.png)
,使
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102931-22020.png)
成立的所有常数
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102931-46958.png)
中,我们把
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102931-46958.png)
的最小值
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102931-59806.png)
叫做函数
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102930-60001.png)
的上确界.
则函数
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102932-29439.png)
的上确界是( )
A.0 | B.![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102932-33692.png) | C.1 | D.2 |
【题文】对于函数
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102919-15912.png)
,解答下述问题:
(1)若函数的定义域为R,求实数a的取值范围;
(2)若函数的值域为
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102919-23139.png)
,求实数a的值;
【题文】(本题小满分10分)设命题
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102912-80717.png)
:函数
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102913-91871.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102913-93841.png)
上单调递增;
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102913-95095.png)
:关于
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102913-49191.png)
的方程
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102913-66688.png)
的解集只有一个子集.若“
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102913-71712.png)
”为真,“
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102913-68659.png)
”为假,求实数
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102914-69021.png)
的取值范围.
【题文】 已知
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102856-73658.png)
且
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102856-90463.png)
,函数
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102857-78325.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102857-19521.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102857-73793.png)
,求函数
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102858-27364.png)
的值域;
(2)利用对数函数单调性讨论不等式
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102858-69714.png)
中
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330102858-34372.png)
的取值范围.
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