题目内容
已知函数
.
(1)当
时,求
的解集;
(2)当
时,
恒成立,求实数
的集合.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824060533290802.png)
(1)当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824060533306338.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824060533321548.png)
(2)当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824060533337504.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824060533321548.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824060533399281.png)
(1)
;(2)
.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824060533399417.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824060533430381.png)
试题分析:
解题思路:(1)利用
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824060533446820.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824060533462636.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824060533477283.png)
规律总结:处理绝对值不等式问题,主要从去掉绝对值符号入手,往往讨论变量的范围去掉绝对值符号,变成分段函数求解问题;证明问题还往往涉及
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824060533508750.png)
试题解析:(1)解:原不等式可化为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824060533524653.png)
当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824060533540409.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824060533555476.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824060533571401.png)
当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824060533586548.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824060533602457.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824060533571401.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824060533586548.png)
当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824060533664458.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824060533680472.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824060533711392.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824060533727577.png)
综上所述:原不等式的解集为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824060533742418.png)
(2)原不等式可化为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824060533758715.png)
∵
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824060533337504.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824060533805650.png)
即
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824060533836719.png)
故
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824060533852696.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824060533337504.png)
当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824060533898454.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824060533914439.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824060533930289.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824060533945362.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824060533930289.png)
∴实数
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824060533399281.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824060534008383.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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