题目
题型:解答题难度:简单来源:不详
已知
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224830-25620.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224830-25727.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224830-36377.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224830-38811.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224831-58382.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224831-13911.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224830-25620.png)
(2)判断
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224830-25620.png)
(3)已知
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224831-15308.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224831-33901.png)
集合
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224832-17655.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224832-44629.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224832-53179.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224832-91217.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224830-25620.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224832-39442.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224833-52706.png)
解析
试题分析:解:(1)令
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224833-28911.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224833-88575.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224833-84188.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224833-90677.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224834-75722.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224834-55030.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224832-91217.png)
(2)函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224830-25620.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224832-39442.png)
证明如下:
设
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224834-82947.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224834-18993.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224834-97147.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224835-59890.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224835-34166.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224835-46633.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224835-89459.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224830-25620.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224832-39442.png)
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224835-66596.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224831-15308.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224830-36377.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224836-78323.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224836-74688.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224836-58898.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224836-93944.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224836-90416.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224835-66596.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224837-85276.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224837-32755.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224837-48798.png)
所以,实数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224832-53179.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224833-52706.png)
点评:对于函数的奇偶性和单调性是高考考查的重点,因此要熟练的运用概念,先看定义域,然后看解析式f(x)与f(-x)的关系来确定奇偶性,同时结合抽象函数的赋值法表示来证明单调性,需要对于变量合理的变形来证明,这是一个难点,要注意积累。属于难度试题。
核心考点
试题【(本小题满分12分)已知对于任意实数满足,当时,.(1)求并判断的奇偶性;(2)判断的单调性,并用定义加以证明;(3)已知,集合,集合,若,求实数的取值范围.】;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
设
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224821-94012.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224822-51428.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224822-77232.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224822-51663.png)
(2)若对于区间
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224822-71199.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224822-50335.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224822-30310.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224819-14786.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224819-37153.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224817-79118.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224817-52398.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224811-81886.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224811-57295.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224801-52364.png)
(1)判断函数
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224801-85095.png)
(2)若关于
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224801-27809.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224801-60693.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224802-30193.png)
(3)若
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224802-73934.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224802-58722.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224802-17722.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190818/20190818224802-63578.png)
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