题目内容
设函数
,其中
。
(1)当
时,求不等式
的解集;
(2)若不等式
的解集为
,求a的值。
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824050237022707.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824050237038392.png)
(1)当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824050237054339.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824050237069695.png)
(2)若不等式
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824050237085553.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824050237100580.png)
(1)
或
(2)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824050237163395.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824050237116521.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824050237147436.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824050237163395.png)
(1)当
时,
可化为
。
由此可得
或
。
故不等式
的解集为
或
。
(2)由
得 ![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824050237381622.png)
此不等式化为不等式组
或![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824050237428865.png)
即
或![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824050237459809.png)
因为
,所以不等式组的解集为![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824050237506735.png)
由题设可得
=
,故![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824050237163395.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824050237054339.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824050237069695.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824050237241493.png)
由此可得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824050237288395.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824050237288379.png)
故不等式
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824050237069695.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824050237116521.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824050237147436.png)
(2)由
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824050237085553.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824050237381622.png)
此不等式化为不等式组
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824050237397884.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824050237428865.png)
即
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824050237444776.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824050237459809.png)
因为
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824050237038392.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824050237506735.png)
由题设可得
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824050237522423.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824050237553219.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824050237163395.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
练习册系列答案
相关题目