题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092646-88644.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092647-27873.png)
(1)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092647-50016.png)
(2)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092647-50016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092647-94870.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092647-55795.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092647-13013.png)
解析
试题分析:(1)先求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092647-50016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092648-27321.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092648-53161.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092648-57545.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092647-55795.png)
试题解析:(1)函数定义域为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092648-16322.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092649-16754.png)
①当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092649-17918.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092649-48223.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092649-76146.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092650-16131.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092647-50016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092650-94698.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092650-28637.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092650-51380.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092647-50016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092650-55672.png)
②当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092651-12225.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092651-83445.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092650-28637.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092651-49746.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092650-51380.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092647-50016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092651-65588.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092650-55672.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092649-76146.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092652-60664.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092647-50016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092652-67702.png)
③当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092652-57108.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092652-34214.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092652-20560.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092647-50016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092653-66892.png)
(2)①当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092649-48223.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092647-50016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092650-94698.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092647-50016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092653-25196.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092647-50016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092647-94870.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092653-52387.png)
由于
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092653-55537.png)
要使
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092647-50016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092647-94870.png)
需满足
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092654-43069.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092654-92403.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092654-50408.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092654-88865.png)
所以当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092654-50408.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092654-88865.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092647-50016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092647-94870.png)
②当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092652-34214.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092647-50016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092647-94870.png)
且
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092655-95417.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092655-67729.png)
所以当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092652-34214.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092647-50016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092647-94870.png)
③当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092651-83445.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092647-50016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092651-65588.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092652-67702.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092653-25196.png)
又因为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092655-42027.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092655-52963.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092655-74052.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092656-48781.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092656-60882.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092647-50016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092651-65588.png)
又因为
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092647-50016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092651-65588.png)
从而当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092651-83445.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092647-50016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092647-94870.png)
综上所述,当
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092656-22275.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092654-88865.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092654-50408.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092647-50016.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092647-94870.png)
核心考点
举一反三
(1)若a=0,判断f(x)的单调性;.
(2)若x>1时,f(x)<0恒成立,求a的取值范围.
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092624-23421.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092624-36538.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092624-91604.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092624-79528.png)
已知
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092615-17835.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092615-54290.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092615-33756.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092615-54290.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092615-11874.png)
(1)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092616-70833.png)
(2)求函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092616-99545.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092607-25954.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092607-77426.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092556-77461.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092556-39755.png)
(1)求
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092556-49126.png)
(2)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092556-45928.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191018/20191018092556-67415.png)
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