【题文】函数的单调减区间为( )A.B.C.D.
题型:难度:来源:
【题文】函数
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331101703-71312.png)
的单调减区间为( )
答案
【答案】A
解析
【解析】
试题分析:要是函数
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331101706-13421.png)
有意义的需要满足:
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331101706-12710.png)
,解得
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331101707-90889.png)
或
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331101707-43859.png)
,所以函数
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331101706-13421.png)
的定义域为
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331101707-51433.png)
;
令
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331101708-67768.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331101708-49032.png)
,因为函数
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331101708-49032.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331101708-56727.png)
是单调递增函数,由复合函数同增异减,要求函数
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331101706-13421.png)
的单调递减区间,即为函数
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331101708-67768.png)
的单调递减区间与函数
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331101706-13421.png)
定义域的交集;函数
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331101708-67768.png)
是开口向上,对称轴为
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331101709-56994.png)
的二次函数,则函数
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331101708-67768.png)
的单调递减区间为
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331101709-45603.png)
,所以函数
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331101706-13421.png)
的单调递减区间为
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331101709-57954.png)
,所以答案选
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331101710-99308.png)
.
考点:1.复合函数的单调性;2.对数函数的单调性;3.二次函数的单调性;4.函数的定义域;5.一元二次不等的解法.
举一反三
【题文】设函数
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331100658-74572.png)
的定义域为
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331100658-25824.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331100658-90408.png)
,值域为
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331100658-73468.png)
,若
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331100659-34224.png)
的最小值为
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331100659-65428.png)
,则实数
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331100700-77323.png)
的值为
.
【题文】函数f(x)=
![](http://img.shitiku.com.cn/uploads/allimg/20200331/20200331100233-92059.png)
的定义域是
.
【题文】已知函数f(x)=|lg(x-1)|若a≠b,f(a)=f(b),则a+2b的取值范围是
.
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