【解析】
试题分析:(1)根据题中条件在a已知的条件下易表示出:
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325191215-27633.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325191218-46727.png)
,观察其中含有一个绝对值,我们要想把绝对值去掉即可:
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325191215-82882.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325191218-38735.png)
,得到一个分段函数,根据先分段后合并的处理原则不难求出各自的范围:当
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325191219-93666.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325191219-98514.png)
;当
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325191219-70430.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325191219-78230.png)
,再合并可得:
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325191215-27633.png)
的值域为
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325191217-80182.png)
;(2)对于含a 的不等式与函数,我们同样去掉绝对值转化为分段函数:
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325191220-28895.png)
,可见当
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325191220-57657.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325191220-88910.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325191215-98304.png)
,得
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325191221-61567.png)
或
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325191218-31985.png)
;
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325191221-23825.png)
或
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325191218-84794.png)
;当
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325191221-64182.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325191220-88910.png)
,得
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325191221-39334.png)
或
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325191220-57657.png)
,合并即可.
试题解析:(1)
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325191215-27633.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325191218-46727.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325191218-38735.png)
;
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325191219-93666.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325191219-98514.png)
;
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325191219-70430.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325191219-78230.png)
;
所以
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325191215-27633.png)
的值域为
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325191217-80182.png)
;
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325191220-28895.png)
;
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325191220-57657.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325191220-88910.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325191215-98304.png)
,得
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325191221-61567.png)
或
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325191218-31985.png)
;
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325191221-23825.png)
或
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325191218-84794.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325191221-64182.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325191220-88910.png)
,得
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325191221-39334.png)
或
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325191220-57657.png)
;
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325191222-60444.png)
综上:
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325191222-70244.png)
或
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325191218-31985.png)
或
![](http://img.shitiku.com.cn/uploads/allimg/20200325/20200325191218-84794.png)
考点:1.绝对值的处理;2.分段函数的应用;3.函数与不等式的运用