题目
题型:解答题难度:一般来源:不详
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024238-64840.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024239-37676.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024239-19451.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024239-48647.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024239-20214.png)
(1)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024239-19544.png)
(2)是否存在实数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024239-86542.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024240-71681.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024240-20253.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024239-86542.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024240-11048.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024239-86542.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024240-11303.png)
解析
试题分析:(1)根据
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024239-37676.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024240-68648.png)
根据对任意
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024239-19451.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024239-20214.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024239-19544.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024241-86146.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024241-94216.png)
利用对任意
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024239-19451.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024239-48647.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024241-40526.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024239-19451.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024241-90372.png)
(2)化简函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024240-71681.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024241-45503.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024242-22672.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024242-23550.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024242-23898.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024240-11303.png)
试题解析:
(1)由
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024238-64840.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024239-37676.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024240-68648.png)
又对任意
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024239-19451.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024239-20214.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024239-19544.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024241-86146.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024242-95398.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024241-94216.png)
又对任意
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024239-19451.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024239-48647.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024241-40526.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024239-19451.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024242-68599.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024241-90372.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024240-11048.png)
(2)由(1)知
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024240-71681.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024241-45503.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024242-22672.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024242-23550.png)
要使函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024243-68359.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024240-20253.png)
只需函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024242-23550.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024240-20253.png)
由指数函数的单调性,有
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024242-23898.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024240-11303.png)
故存在实数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024239-86542.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024240-11303.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024240-71681.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024240-20253.png)
核心考点
试题【已知函数满足,对任意都有,且.(1)求函数的解析式;(2)是否存在实数,使函数在上为减函数?若存在,求出实数的取值范围;若不存在,说明理由.】;主要考察你对一次函数的图象和性质等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024232-72301.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024233-17555.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024229-86031.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024229-83158.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024229-46817.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024229-89941.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024223-55226.png)
(Ⅰ)令
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024223-47784.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024223-77849.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024223-44149.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024223-44149.png)
(Ⅱ)求函数的值域,并求函数取得最小值时的
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024224-57322.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024219-30927.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024220-57413.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024220-62656.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819024216-93742.png)
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