【题文】设是偶函数,是奇函数,那么的值为( )A.1B.-1C.D.
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【题文】设
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327003625-96761.png)
是偶函数,
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327003626-50556.png)
是奇函数,那么
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327003626-24055.png)
的值为( )
A.1 | B.-1 | C.![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327003626-68948.png) | D.![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327003626-51642.png) |
答案
【答案】D
解析
【解析】由已知中f(x)=lg(10
x+1)+ax为偶函数,
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327003626-50556.png)
是奇函数,结合函数奇偶性的性质,可以构造关于a,b的方程,解方程求出a,b的值,可得答案.
解:∵f(x)=lg(10
x+1)+ax为偶函数
∴f(-x)=f(x)
即lg(10
x+1)+ax=lg(10
-x+1)-ax
解得a=-
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327003627-44220.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327003626-50556.png)
是奇函数,
∴g(0)=
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327003627-35367.png)
解得b=1
∴a+b=
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327003627-44220.png)
故选D
举一反三
【题文】已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327003617-10605.png)
,且
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327003617-64728.png)
,那么
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327003618-82827.png)
等于( )
A 10 B.-10 C.-18 D.-26
【题文】设
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327003515-94360.png)
是偶函数,
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327003516-32484.png)
是奇函数,那么
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327003516-70428.png)
的值为( )
A.1 | B.-1 | C.![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327003516-86663.png) | D.![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327003517-69871.png) |
【题文】已知定义在R上的奇函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327003510-10929.png)
,满足
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327003511-19519.png)
,且在区间[0,2]上是增函
数,则( ).
【题文】已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327003454-57737.png)
定义域为R,则
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327003454-18279.png)
一定为 (
A.偶函数 | B.奇函数 |
C.非奇非偶函数 | D.既奇又偶函数 |
【题文】已知定义在R上的奇函数
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327003450-25053.png)
,满足
![](http://img.shitiku.com.cn/uploads/allimg/20200327/20200327003450-59610.png)
,且在区间[0,2]上是增函
数,则( ).
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