题目
题型:解答题难度:简单来源:不详
对定义在
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194925-99222.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194925-13976.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194925-76199.png)
① 对任意的
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194925-78346.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194925-17504.png)
② 当
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194926-58316.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194926-56053.png)
已知函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194926-31356.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194926-89831.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194925-99222.png)
(1)试问函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194927-91478.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194927-79160.png)
(2)若函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194927-14236.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194927-79160.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194927-60204.png)
(3)在(2)的条件下,是否存在实数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194927-98873.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194928-58632.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194927-98873.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194928-96117.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194928-61185.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194926-58316.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194928-87846.png)
所以函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194927-91478.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194927-79160.png)
(2)因为函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194927-14236.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194927-79160.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194928-10847.png)
根据②有
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194928-66081.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194929-73637.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194929-67228.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194929-70841.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194929-21520.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194929-82001.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194930-41491.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194930-82852.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194930-42087.png)
于是
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194930-29445.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194930-39713.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194931-86774.png)
于是
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194931-28668.png)
另解:因为函数
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194927-14236.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194931-43689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194928-10847.png)
根据②有
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194931-62974.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194931-97015.png)
取
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194932-51194.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194932-21291.png)
于是
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194931-28668.png)
(3)【理科】根据(2)知
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194931-28668.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194932-53068.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194932-72551.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194932-11122.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194933-44546.png)
由图形可知:当
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194933-51711.png)
当
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194933-15359.png)
因此,方程不存在两解。………………………………………………………18分
【文科】根据(2)知
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194931-28668.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194932-53068.png)
由
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194932-72551.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194932-11122.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194933-94751.png)
因此,当
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194933-51711.png)
解析
核心考点
试题【(本题共3小题,满分18分。第1小题满分4分,第2小题满分7分,第3小题7分)对定义在上,并且同时满足以下两个条件的函数称为函数.① 对任意的,总有;② 当时,】;主要考察你对指数函数图象及性质等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194922-51334.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194922-50449.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194922-73933.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194923-54372.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194916-22992.png)
定义
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194916-29097.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194916-42567.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194917-70856.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194917-42522.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194916-29097.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194917-84583.png)
(1)直接写出不等式
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194917-41668.png)
(2)求证:所有的点
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194918-33645.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194918-35634.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194902-93033.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194903-66313.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194903-94990.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194903-35540.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194903-98085.png)
1、(理)求线段
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194903-96053.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194904-29661.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194904-52321.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194904-14761.png)
(文)求点
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194904-26545.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194904-42371.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194905-51023.png)
2、(理)定义:“圆”是所有到定点“距离”为定值的点组成的图形,
求“圆周”上的所有点到点
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194905-29570.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194905-69977.png)
(文)求线段
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194903-96053.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194904-29661.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194904-52321.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194904-14761.png)
3、(理)点
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194904-26545.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194904-42371.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194905-96469.png)
(文)定义:“圆”是所有到定点“距离”为定值的点组成的图形,点
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194904-26545.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194904-42371.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194906-95158.png)
(说明所给图形小正方形的单位是1)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194906-57789.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194900-46241.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194900-93877.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194901-67223.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194901-90840.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194901-63749.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194901-34211.png)
为了研究某种癌细胞的繁殖规律和一种新型抗癌药物的作用,将癌细胞注入一只小白鼠体内进行实验,经检测,癌细胞的繁殖规律与天数的关系如下表.已知这种癌细胞在小白鼠体内的个数超过
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194856-35229.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190819/20190819194857-63392.png)
天数![]() | 1 | 2 | 3 | 4 | 5 | 6 | 7 | … |
癌细胞个数![]() | 1 | 2 | 4 | 8 | 16 | 32 | 64 | … |
(2)若在第10天,第20天,第30天,……给小白鼠注射这种药物,问第38天小白鼠是否仍然存活?请说明理由.
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