题目
题型:解答题难度:一般来源:不详
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040007-63037.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040007-42671.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040008-51076.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040008-75636.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040008-61671.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040008-66892.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040008-34671.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040008-23079.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040007-42671.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040007-63037.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040009-97083.png)
(1)求证:函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040009-52561.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040009-25497.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040009-97083.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040007-42671.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040009-97083.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040009-29718.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040009-54904.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040010-41337.png)
(3)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040010-21847.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040010-62882.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040009-97083.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040010-58606.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040010-79357.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040010-57480.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040011-80140.png)
解析
试题分析:(1)根据题意可将函数中的绝对值去掉可得一个分段函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040011-18456.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040011-37262.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040011-14023.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040011-55708.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040012-37631.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040012-27502.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040010-41337.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040012-34910.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040009-97083.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040012-35774.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040008-75636.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040012-25465.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040013-85874.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040013-84574.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040012-25465.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040013-78503.png)
试题解析:(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040011-37262.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040011-14023.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040011-55708.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040012-37631.png)
∴ 存在闭区间
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040013-28546.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040013-35650.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040014-54140.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040009-54904.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040014-80217.png)
解得
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040010-57480.png)
(3)存在闭区间
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040012-35774.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040008-75636.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040012-25465.png)
都有
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040013-85874.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040014-92542.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040014-78811.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040012-25465.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040014-93296.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040014-89626.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040015-31373.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040015-18793.png)
① 当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040015-19344.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040015-76278.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040015-50130.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040016-31191.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040016-39161.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040016-98737.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040016-10549.png)
由题意知,
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040011-80140.png)
②当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040016-86642.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040017-78877.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040017-19005.png)
综上,
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040011-80140.png)
核心考点
试题【对定义在区间上的函数,若存在闭区间和常数,使得对任意的,都有,且对任意的都有恒成立,则称函数为区间上的“型”函数.(1)求证:函数是上的“型”函数;(2)设是(】;主要考察你对函数的单调性与最值等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035958-74748.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035958-66532.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035958-66532.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035959-26483.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035959-70570.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035958-66532.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035959-40660.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035959-46361.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035959-40660.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035959-73416.png)
(1)求曲线
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035959-73416.png)
(2)已知点
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040000-27969.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040000-16427.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040000-40029.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035959-73416.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040000-38432.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818040000-21618.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035949-91022.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035949-91022.png)
(1)对任意的
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035950-46983.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035949-91022.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035950-29691.png)
(3)若
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035950-82786.png)
(1)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035949-91022.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035950-34337.png)
(2)函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035950-12762.png)
(3)若
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035949-91022.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035951-59268.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035951-27259.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035951-74819.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035951-26380.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035945-42724.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035945-60998.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035946-39916.png)
(2)问是否存在实数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035946-30279.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035946-29688.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035946-79727.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035946-39916.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035946-33837.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035947-49423.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035946-30279.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035946-29688.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035942-83790.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035942-58052.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035942-61802.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035942-80905.png)
(Ⅰ)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035942-83790.png)
(Ⅱ)解不等式
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035943-29014.png)
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