题目内容
已知函数
.
(1)当
时,解不等式
;
(2)若
时,
,求a的取值范围.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824043921662915.png)
(1)当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824043921678346.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824043921678514.png)
(2)若
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824043921694543.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824043921709552.png)
(1)
;(2)[-7,7].
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824043921725614.png)
试题分析:本题主要考查绝对值不等式的解法、不等式恒成立等基础知识,考查学生分析问题解决问题的能力、转化能力、计算能力.第一问,先把a=-1代入,先写出
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824043921678514.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824043921694543.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824043921772429.png)
试题解析:(1)当a=-1时,不等式为|x+1|-|x+3|≤1.
当x≤-3时,不等式化为-(x+1)+(x+3)≤1,不等式不成立;
当-3<x<-1时,不等式化为-(x+1)-(x+3)≤1,解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824043921787583.png)
当x≥-1时,不等式化为(x+1)-(x+3)≤1,不等式必成立.
综上,不等式的解集为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824043921725614.png)
(2)当x∈[0,3]时,f(x)≤4即|x-a|≤x+7,
由此得a≥-7且a≤2x+7.
当x∈[0,3]时,2x+7的最小值为7,
所以a的取值范围是[-7,7]. 10分
![](http://thumb2018.1010pic.com/images/loading.gif)
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