题目
题型:解答题难度:简单来源:不详
定义在
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224531-72238.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224531-32819.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224532-15570.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224532-29477.png)
②
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224531-32819.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224531-72238.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224532-58074.png)
(Ⅰ)求
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224532-60205.png)
(Ⅱ)证明
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224531-32819.png)
(Ⅲ)解不等式
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224532-26481.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224533-62776.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224533-56298.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224533-99114.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224533-87457.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224533-55610.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224531-32819.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224534-94791.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224534-60061.png)
解析
试题分析:(Ⅰ)取
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224534-23887.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224534-19710.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224533-62776.png)
(Ⅱ)定义域
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224533-56298.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224533-99114.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224533-87457.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224533-55610.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224531-32819.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224534-94791.png)
(Ⅲ)不等式可化为
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224534-80065.png)
∴解集为
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224534-60061.png)
点评:一般地,抽象函数所满足的关系式,应看作给定的运算法则,则变量的赋值或变量及数值的分解与组合都应尽量与已知式或所给关系式及所求的结果相关联
核心考点
试题【(本题满分12分)定义在上的函数满足:①对任意都有;② 在上是单调递增函数;③.(Ⅰ)求的值;(Ⅱ)证明为奇函数;(Ⅲ)解不等式.】;主要考察你对函数的奇偶性与周期性等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224528-27180.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224528-48411.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224528-31416.png)
A.1个 | B.2个 | C.3个 | D.0个 |
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224524-85930.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224524-14229.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224524-38163.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224524-27432.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224525-99525.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224525-50642.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224520-74210.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224520-58370.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224520-18571.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224520-79100.png)
A.1 | B.![]() | C.2 | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224519-70139.png)
A.![]() | B.x>2 |
C.x>2或![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224516-55679.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224517-51760.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224517-46458.png)
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