【题文】已知函数的定义域为,,对任意,都有,则( )A.B.C.D.
题型:难度:来源:
【题文】已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325080224-53372.png)
的定义域为
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325080224-36388.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325080225-16147.png)
,对任意
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325080225-39343.png)
,都有
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325080225-97412.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325080225-99350.png)
( )
答案
【答案】B
解析
【解析】此题考查等差数列的应用和利用裂项相消法求非特殊数列的和的公式,由已知可以得出
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325080227-79828.png)
是一个首项为3公差为2的等差数列。由已知得
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325080228-65589.png)
且
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325080225-16147.png)
,所以
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325080228-91657.png)
,即
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325080228-93481.png)
,所以
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325080229-12596.png)
,所以
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325080229-83204.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325080229-15756.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325080229-69006.png)
,选B
举一反三
【题文】已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325080217-22543.png)
,若
f[
f(
x)]=2,则
x的取值范围是
A.![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325080217-15744.png) | B.[-1,1] |
C.(-∞,-1)∪(1,+∞) | D.{2}∪[-1,1] |
【题文】已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325080203-16764.png)
,若
f[
f(
x)]=2,则
x的取值范围是
A.![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325080203-48102.png) | B.[-1,1] |
C.(-∞,-1)∪(1,+∞) | D.{2}∪[-1,1] |
【题文】函数
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325080140-55907.png)
的单调递增区间为
。
【题文】函数
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325080134-86275.png)
的单调递增区间为
。
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