题目
题型:解答题难度:简单来源:不详
已知
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182031-66109.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182032-73910.png)
(Ⅰ)当
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182032-10514.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182032-56526.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182032-15506.png)
(Ⅱ)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182032-97816.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182033-68025.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182033-48338.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182033-29758.png)
解析
试题分析:(Ⅰ)由题意,
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182033-58863.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182033-41691.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182034-29956.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182034-33968.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182034-18217.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182034-13394.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182035-36448.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182035-97832.png)
综上,所求解集为
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182033-48338.png)
(Ⅱ)设此最小值为
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182035-44618.png)
①当
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182035-24856.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182035-20291.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182035-28715.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182036-37250.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182036-63814.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182036-82405.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182036-76674.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182036-89360.png)
②当
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182037-63267.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182036-76674.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182037-85106.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182037-46187.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182037-20469.png)
③当
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182038-34460.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182036-76674.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182038-12296.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182038-84380.png)
若
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182038-34974.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182039-58823.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182039-89886.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182036-82405.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182036-76674.png)
由此得
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182039-32791.png)
若
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182039-26849.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182039-38225.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182040-52549.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182039-89886.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182036-82405.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182040-75713.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182040-69916.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182040-72506.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182036-82405.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182040-99682.png)
因此,当
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182039-26849.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182039-32791.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182041-78134.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182041-75901.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182041-36131.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182041-78134.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182041-75966.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182041-20519.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182039-32791.png)
综上所述,所求函数的最小值
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182033-29758.png)
点评:求解含绝对值的不等式或函数问题,关键是通过讨论去掉绝对值符号,讨论的时候要注意做到“不重不漏”.
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182021-50651.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182021-99824.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182021-55897.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182021-35550.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182022-24314.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182022-12537.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182021-50651.png)
(3)当
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182022-17389.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182022-90395.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182015-41143.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182015-10133.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182015-90855.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182015-47955.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182015-37328.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182015-66024.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182016-68625.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182015-47955.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182016-33257.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182008-71797.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182009-35422.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182009-78396.png)
(2)若对任意的
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182009-62028.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182009-81676.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182010-81950.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182010-17576.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182010-73173.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182010-69744.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182011-92348.png)
(3)是否存在
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182011-99650.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182009-78396.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182011-86878.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182011-64975.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182012-66589.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182011-86878.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182012-90173.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182012-41811.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182006-67163.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182000-16852.png)
(Ⅰ)讨论函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182000-80085.png)
(Ⅱ)当
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182000-29316.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182000-80085.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182000-21031.png)
(Ⅲ)若
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182000-80085.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182000-62842.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182001-99856.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182001-51279.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182001-72347.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182001-79301.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819182002-95714.png)
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