题目
题型:解答题难度:简单来源:不详
已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195702-24132.png)
(I)证明:对任意实数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195702-53222.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195702-33756.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195703-78000.png)
(II)若方程
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195703-57342.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195703-91365.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195703-61186.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195703-19699.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195703-47856.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195703-69238.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195703-58002.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195703-32194.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195703-37121.png)
由题意可知,只要证明函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195703-25257.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195703-85247.png)
任取
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195703-60892.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195703-93573.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195703-21601.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195703-65798.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195704-86167.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195704-52189.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195704-82628.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195704-86420.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195704-32164.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195703-85247.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195704-86420.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195702-53222.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195704-63836.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195704-68604.png)
(II)若方程
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195704-77875.png)
也就是方程
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195704-79238.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195704-41301.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195704-61049.png)
(1) 若
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195704-60938.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195704-55433.png)
(2) 若
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195704-14271.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195705-84695.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195705-33434.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195705-61614.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195705-76060.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195705-84621.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195705-71313.png)
(3) 若
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195704-14271.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195705-23916.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195705-53859.png)
………11分
综上:实数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195703-91365.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195705-29316.png)
解析
核心考点
试题【本小题满分12分)已知函数是偶函数.(I)证明:对任意实数,函数的图象与直线最多只有一个交点;(II)若方程有且只有一个解,求实数的取值范围.】;主要考察你对指数函数图象及性质等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195701-83425.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195701-14401.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195701-37960.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195657-46710.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195655-82369.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195655-44127.gif)
(1
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195655-96373.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195655-92631.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195655-56188.gif)
(2)当年产量为何值时,工厂的年利润最大,其最大值是多少?
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195651-15250.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195651-85729.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195651-16216.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195651-53248.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195651-15250.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195651-15250.gif)
已知定义域为
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195642-51421.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195642-88551.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195643-30330.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195643-75377.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195643-62099.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195643-23033.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195644-79164.gif)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195644-62559.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195642-88551.gif)
(3)求不等式
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819195644-52927.gif)
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