题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085748-43434.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085748-66918.png)
(1)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085748-96072.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085748-39061.png)
(2)讨论函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085748-96072.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085748-39061.png)
(3)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085748-92486.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085748-39061.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085749-17584.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085749-58706.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085749-92110.png)
(2)单调递增区间为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085749-45413.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085749-81751.png)
递减区间为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085749-81754.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085749-51337.png)
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085749-76177.png)
解析
试题分析:(1)由已知条件得到
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085750-29710.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085750-45076.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085748-96072.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085748-39061.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085750-94207.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085750-93449.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085750-91218.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085748-96072.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085748-96072.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085750-73257.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085748-96072.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085748-96072.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085749-17584.png)
试题解析:(1)可知
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085750-99822.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085750-88050.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085751-46117.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085750-45076.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085751-39052.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085751-20761.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085751-35038.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085751-51615.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085751-63296.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085752-36165.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085752-67703.png)
所以函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085748-96072.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085748-39061.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085752-45131.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085752-71195.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085750-91218.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085752-11137.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085753-12049.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085753-67268.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085753-40199.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085752-36165.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085753-94536.png)
所以函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085748-96072.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085749-45413.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085749-81751.png)
同理递减区间为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085749-81754.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085749-51337.png)
(3)由
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085750-73257.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085753-74852.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085753-88906.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085753-86646.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085754-20266.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085754-70658.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085754-68400.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085754-61604.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085754-46835.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085755-88110.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085755-96680.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085755-41042.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085755-81560.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085755-87899.png)
结合函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085748-96072.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085749-17584.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085749-76177.png)
【考点定位】本题以复合函数为载体,考查函数的定义域、单调区间以及不等式的求解,从中渗透了二次不等式的求解,在求定义域时考查了分类讨论思想,以及利用作差法求解不等式的问题,综合性强,属于难题.
核心考点
举一反三
已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085732-62089.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085732-41170.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085732-58385.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085732-58385.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085733-61823.png)
设函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085720-96688.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085721-21462.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085721-89651.png)
(Ⅰ)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085721-24343.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085721-74330.png)
(Ⅱ)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085721-74330.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085722-52848.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085721-21462.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085712-45587.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085713-83881.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085713-33767.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085713-78909.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085713-89802.png)
A.![]() | B.![]() | C.![]() | D.![]() |
(1)讨论函数f(x)的单调性;
(2)若函数f(x)在区间(1,2)是增函数,求a的取值范围.
已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085649-10774.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085649-10225.png)
(1)当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085649-30273.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085650-40689.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085650-40689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085650-62661.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018085650-26634.png)
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