题目
题型:解答题难度:简单来源:不详
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002100-80093.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002100-13759.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002100-16325.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002100-94329.png)
(1)函数
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002100-34953.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002100-80093.png)
(2)设函数
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002101-37332.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002101-21700.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002101-91030.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002102-14996.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002102-63572.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002102-63572.png)
解析
试题分析:(Ⅰ)当
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002102-34742.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002100-94329.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002102-50399.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002102-22127.png)
f(x)=
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002103-33375.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002103-42825.png)
令
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002103-75765.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002103-44582.png)
因此,不存在x
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002102-14996.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002103-42825.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002101-91030.png)
(Ⅱ)f(x)=lg
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002103-71065.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002104-34721.png)
若f(x)= lg
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002103-71065.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002102-14996.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002102-14996.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002104-98829.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002103-71065.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002104-34721.png)
整理得存在x
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002102-14996.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002103-44582.png)
(1)若a-2=0即a=2时,方程化为8x+4=0,解得x=-
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002104-18059.png)
(2)若a-2
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002104-58805.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002102-14996.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002104-36934.png)
解得a
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002102-14996.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002105-64761.png)
综上,a
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002102-14996.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002102-63572.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002102-63572.png)
点评:综合题,本题以新定义函数为载体,综合考查对数函数的性质,方程解的讨论,对考生数学式子变形能力要求较高。本题较难。
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002054-70518.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002055-52554.png)
(I)若
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002055-97531.png)
(II)若
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002055-72165.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002052-10516.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002052-66959.jpg)
A.{x|-3 <x <-1} | B.{x|-3 <x <0} |
C.{x|-3 ≤x <0} | D.{x|x <-3} |
A.![]() | B.![]() | C.![]() | D.![]() |
(1)很小的实数可以构成集合;
(2)集合
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002046-43435.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002046-11480.png)
(3)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002046-99490.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002046-36146.png)
(4)集合
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002047-90820.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002044-29708.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002044-13172.png)
![](http://img.shitiku.com.cn/uploads/allimg/20190815/20190815002045-75973.png)
A.6个 | B.5个 | C.8个 | D.7个 |
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