题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055201-24039.gif)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055201-34527.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055201-58515.gif)
(2)若对任意
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055201-95998.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055201-47498.gif)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055201-34527.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055202-40384.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055202-46641.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055202-33805.gif)
当且仅当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055202-93261.gif)
(2)令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055202-84625.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055202-56921.gif)
(ⅰ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055203-95184.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055201-95998.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055203-23591.gif)
故
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055203-24184.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055203-19653.gif)
所以,
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055201-95998.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055204-30348.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055204-56207.gif)
(ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055204-19979.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055204-58910.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055204-65193.gif)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055205-46761.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055205-12514.gif)
此时,若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055205-31092.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055205-56901.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055203-24184.gif)
所以,
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055205-31092.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055205-83370.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055206-42493.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055204-56207.gif)
综上,满足条件的
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055206-13466.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055206-66071.gif)
解析
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055146-37334.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055146-96510.gif)
(1) 设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055146-69339.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055146-70706.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055146-45601.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055146-80132.gif)
(2) 证明: 当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055146-14653.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055147-34429.gif)
(3) 设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055147-44853.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055147-83488.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055147-93663.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055147-86717.gif)
已知定义在
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055132-76741.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055133-86170.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055133-26312.gif)
(Ⅰ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055133-94042.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055133-76578.gif)
求证:当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055133-13391.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055134-88929.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055134-30169.gif)
(Ⅱ)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055134-77526.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055134-73182.gif)
求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055133-26312.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055123-88595.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055123-30634.gif)
(Ⅰ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055123-30634.gif)
(Ⅱ)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055123-23045.gif)
(Ⅲ)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055123-80041.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055124-87782.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055113-90763.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055113-38661.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055114-15203.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055114-56190.gif)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055114-15203.gif)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055114-60236.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055114-73917.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055115-88877.gif)
(3)是否存在实数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055115-45667.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055115-84025.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055115-31480.gif)
在定义域[a,b] 上的值域恰为[a,b],若存在,求出k的范围;若不存在,说明理由.
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055105-44929.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055105-93652.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055105-30033.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055106-72241.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018055106-42073.png)
的解集为
A.(-1,1) | B.(-1,+![]() | C.(-![]() | D.![]() ![]() |
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