题目内容
设f (x)=|2-x2|,若0<a<b且f (a)="f" (b),则a+b的取值范围是( )
A.(0,2) | B.(![]() | C.(2,4) | D.(2,2![]() |
D
解:
当x<0时,f(x)= -x2+2(- 2 <x<0)
x2-2(x≤- 2 )
∴f(x)在(-∞,- 2 )递增;在(- 2 ,0)
∵a<b<0,且f(a)=f(b),
∴-a≤-
,b>2-
且a2-2="-" a2+2
解得a=
;2-
<b<![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823215127294344.png)
故选D
当x<0时,f(x)= -x2+2(- 2 <x<0)
x2-2(x≤- 2 )
∴f(x)在(-∞,- 2 )递增;在(- 2 ,0)
∵a<b<0,且f(a)=f(b),
∴-a≤-
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823215127294344.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823215127294344.png)
解得a=
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823215127294344.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823215127294344.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823215127294344.png)
故选D
![](http://thumb2018.1010pic.com/images/loading.gif)
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