【题文】 在下列函数①②③④⑤中,满足“对任意的,,则恒成立”的函数是________.(填上所有正确的序号)
题型:难度:来源:
【题文】 在下列函数①
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330091358-73504.png)
②
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330091359-29240.png)
③
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330091359-28468.png)
④
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330091400-35457.png)
⑤
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330091400-36094.png)
中,满足“对任意的
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330091400-46393.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330091400-78738.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330091400-50543.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330091401-25428.png)
恒成立”的函数是________.(填上所有正确的序号)
答案
【答案】①③
解析
【解析】
试题分析:首先满足“对任意的
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330091400-46393.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330091400-78738.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330091400-50543.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330091401-25428.png)
恒成立”的函数的图象在区间
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330091400-50543.png)
上是下凸的,如下示意图所示:
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330091401-58002.png)
而函数②
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330091359-29240.png)
④
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330091400-35457.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330091359-29240.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330091400-36094.png)
的图象在区间
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330091400-50543.png)
上是上凸的,只有函数①
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330091358-73504.png)
③
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330091359-28468.png)
符合题意,所以答案应填:①③.
考点:函数的图象.
举一反三
【题文】 在下列函数①
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330091326-68070.png)
②
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330091327-25197.png)
③
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330091328-49740.png)
④
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330091328-33100.png)
⑤
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330091328-79801.png)
中,满足“对任意的
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330091329-34656.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330091329-73133.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330091330-91564.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330091330-79058.png)
恒成立”的函数是________.(填上所有正确的序号)
【题文】函数
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330091209-12904.png)
的定义域为_____
__.
【题文】函数
![](http://img.shitiku.com.cn/uploads/allimg/20200330/20200330091039-62154.png)
的定义域为_____
__.
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