题目
题型:不详难度:来源:
已知
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004554-65550.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004554-12838.png)
(2)当
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004554-20478.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004554-91827.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004555-45775.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004555-22867.png)
果不存在,请说明理由;
(3)当
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004555-71179.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004555-76744.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004556-58538.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004556-60466.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004556-20911.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004556-79236.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004557-67579.png)
解析
试题分析:(1)根据所求只要判定函数的奇偶性即可,结合定义来证明。同时对于底数a进行分类讨论得到最值。
(2)结合单调性来得到函数的不等式,进而求解取值范围。
解:(1)由
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004557-92260.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004557-34954.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004557-46447.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004558-88309.png)
∴f(x)为奇函数,∴
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004556-60466.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004558-29754.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004558-78868.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004558-27796.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004558-55520.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004558-28040.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004559-85026.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004559-16477.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004559-48354.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004600-79900.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004556-79236.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004600-58188.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004600-88671.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004556-20911.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004556-79236.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004600-22171.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004601-30839.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004559-48354.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004601-26512.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004556-79236.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004600-58188.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004600-88671.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004556-20911.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004556-79236.png)
(3)由(1)及
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004601-77721.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004601-33678.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004559-16477.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004556-79236.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004600-58188.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004602-36990.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004602-69548.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004556-58538.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004557-67579.png)
点评:解决该试题的关键是通过第一问的结构提示我们选择判定函数奇偶性,进而得到求解。同时对于底数a进行分类讨论得到函数的最值问题。
核心考点
试题【(本小题满分12分)已知 (1)求的值;(2)当(其中,且为常数)时,是否存在最小值,如果存在求出最小值;如果不存在,请说明理由; (3)当时,求满足不等式的】;主要考察你对函数的相关概念等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004541-39526.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004541-65983.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004533-51914.png)
A.![]() | B.![]() | C.![]() | D.![]() |
A.![]() ![]() |
B.![]() ![]() |
C.![]() ![]() ![]() |
D.![]() ![]() ![]() ![]() ![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004454-87916.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004454-39593.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004454-25342.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004454-98534.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004455-25436.png)
已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004427-93617.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004427-89709.png)
(1)求常数
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004427-99460.png)
(2)求使
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205004427-73931.png)
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