题目内容
已知函数
的值域为[0,+∞),若关于x的不等式f(x)<c的解集为(m,m+6),则实数c的值为( )
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044521961588.png)
A.7 |
B.8 |
C.9 |
D.10 |
C
由题意知f(x)=x2+ax+b=![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044521976490.png)
∵f(x)的值域为[0,+∞),∴
,即
,∴f(x)=![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044522085349.png)
又∵f(x)<c. ∴
,即![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044522117508.png)
∴![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044522132700.png)
解得,∴c=9,选C.
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044521976490.png)
∵f(x)的值域为[0,+∞),∴
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044522070357.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044522070319.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044522085349.png)
又∵f(x)<c. ∴
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044522101398.png)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044522117508.png)
∴
![](http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824044522132700.png)
解得,∴c=9,选C.
![](http://thumb.zyjl.cn/images/loading.gif)
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题目内容
A.7 |
B.8 |
C.9 |
D.10 |