题目内容
设奇函数
在
上是增函数,且
,若
对所有的
都成立,当
时,则
的取值范围是( )
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823232122782491.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823232122798323.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823232122813534.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823232122845806.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823232122860462.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823232122876458.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823232122907267.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
C
解:若函数f(x)≤t2-2at+1对所有的x∈[-1,1]都成立,由已知易得f(x)的最大值是1,
∴1≤t2-2at+1?2at-t2≤0,设g(a)=2at-t2(-1≤a≤1),欲使2at-t2≤0恒成立,则g(-1)≤0,且g(1)≤0,
所以t≥2或t=0或t≤-2.答案C
∴1≤t2-2at+1?2at-t2≤0,设g(a)=2at-t2(-1≤a≤1),欲使2at-t2≤0恒成立,则g(-1)≤0,且g(1)≤0,
所以t≥2或t=0或t≤-2.答案C
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