题目
题型:解答题难度:一般来源:不详
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035039-31554.png)
(I)用定义证明函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035039-41103.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035039-61729.png)
(II)求
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035039-41103.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035040-82417.png)
答案
解析
试题分析:(I)先求出
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035039-41103.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035040-11748.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035040-65151.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035040-15878.png)
(II)利用函数单调性
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035039-41103.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035040-82417.png)
试题解析:解:(I)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035040-85740.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035041-96546.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035041-73391.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035041-27783.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035041-80492.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035041-59804.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035041-59318.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035042-47754.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035041-59804.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035042-60922.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035042-38003.png)
根据函数单调性的定义知:函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035041-73391.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035039-61729.png)
(II)∵ :函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035041-73391.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035039-61729.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035041-73391.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035040-82417.png)
∴当x=-1时,
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035042-79485.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035031-35403.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035031-72804.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035032-60526.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035032-71029.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035032-52156.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035032-79785.png)
(2)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035031-35403.png)
(3)当
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035032-81744.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035033-30334.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035025-63363.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035025-17116.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035026-26817.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035026-22934.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035026-27571.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035026-44815.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035026-27450.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035027-77950.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035027-33449.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035027-22871.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035016-76640.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035016-16383.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035016-65278.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035016-32699.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035016-48865.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035016-69731.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035017-49642.png)
(2)判断函数的奇偶性;
(3)用函数单调性的定义证明函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035017-43506.png)
(4)若
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035017-48217.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035017-42989.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035005-27365.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035005-29686.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035005-90837.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035006-19396.png)
(2)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035006-67414.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035006-13359.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035006-21252.png)
(3)若存在实数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035006-31464.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035007-13036.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035007-52536.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035007-73371.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818035002-23543.png)
A.是奇函数,且在![]() |
B.是奇函数,且在![]() |
C.是偶函数,且在![]() |
D.是偶函数,且在![]() |
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