【题文】已知是定义在上的偶函数,当时,,则不等式的解集为( )A.B.C.D.
题型:难度:来源:
【题文】已知
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325202854-75703.png)
是定义在
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325202854-20573.png)
上的偶函数,当
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325202855-13499.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325202855-43777.png)
,则不等式
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325202856-57732.png)
的解集为( )
答案
【答案】D
解析
【解析】
试题分析:由当
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325202857-32486.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325202857-96026.png)
,可得:f(x)为增函数,又由f(x)定义在R上的偶函数,可得:f(x)>0时,x>1,或x<-1,故
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325202858-34001.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325202858-38500.png)
,或
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325202858-21063.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325202857-32486.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325202857-96026.png)
,∴f(1)=0,
又∵当
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325202857-32486.png)
时,f(x)为增函数,又是定义在R上的偶函数,
故f(x)>0时,x>1,或x<-1,
故
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325202856-57732.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325202858-38500.png)
,或
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325202859-22530.png)
,解得:
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325202859-87129.png)
.
考点:对数函数的单调性与特殊点;奇偶性与单调性的综合.
举一反三
【题文】已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325202844-76452.png)
是
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325202844-69386.png)
上的偶函数,且
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325202844-72948.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325202845-60534.png)
上是减函数,若
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325202845-63946.png)
,
则
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325202845-30437.png)
的取值范围是( )
【题文】(本小题满分12分)设
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325202831-88494.png)
.
(1)在下列直角坐标系中画出
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325202831-20846.png)
的图象;
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325202832-40843.jpg)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325202832-48966.png)
,求
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325202832-62940.png)
的值;
(3)用单调性定义证明在
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325202833-29968.png)
时单调递增.
【题文】(本小题满分14分)已知
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325202748-42221.png)
.
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325202749-99910.png)
,求
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325202749-73803.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325202750-73681.png)
的值;
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325202749-99910.png)
,判断
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325202750-74665.png)
的奇偶性;
(3)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325202750-93929.png)
在其定义域
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325202751-11045.png)
上是增函数,
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325202751-57648.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325202751-79773.png)
,求
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325202752-60155.png)
的取值范围.
【题文】知
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325202719-42304.png)
,且
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325202719-56784.png)
,设
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325202719-18252.png)
,则有( )
A.P<M<N | B.M<P<N | C.N<P<M | D.P<N<M |
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