题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184214-88272.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184215-15061.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184214-88272.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184214-88272.png)
(1)存在幂函数是对等函数;
(2)存在指数函数是对等函数;
(3)对等函数的积是对等函数.
那么,在上述命题中,真命题的个数是( )
A.0; | B.1; | C.2; | D.3. |
答案
解析
设
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184215-41388.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184215-48007.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184215-25810.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184215-74535.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184215-41388.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184216-29424.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184216-52467.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184216-53524.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184217-99697.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184217-64467.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184217-15480.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184217-33967.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184218-92886.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184218-86125.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184218-55504.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184218-86139.png)
所以(3)正确
故正确答案为C
核心考点
试题【若函数满足=||,则称为对等函数,(1)存在幂函数是对等函数;(2)存在指数函数是对等函数;(3)对等函数的积是对等函数.那么,在上述命题中,真命题的个数是( 】;主要考察你对函数的相关概念等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184203-65004.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184204-40118.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184204-86923.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184204-52350.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184204-66818.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184205-29952.png)
A.![]() | B.![]() |
C.0 | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184137-86519.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184138-40477.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184138-44385.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184138-93031.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184139-35548.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184137-86519.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184138-40477.gif)
如果定义域为
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184139-43619.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184139-46627.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184139-43619.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184139-68870.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184139-68870.gif)
如果定义域为R的函数
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184137-86519.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184140-24633.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184140-42921.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184140-59672.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184137-86519.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184141-74784.gif)
对于两个定义域相同的函数
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184114-45630.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184114-70629.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184114-26216.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184114-72097.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184115-98702.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184115-74334.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184115-28126.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184115-98702.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184114-45630.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184114-70629.gif)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184114-45630.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184115-64649.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184115-88828.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184114-70629.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184115-88828.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184115-98702.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184115-70319.gif)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184115-98702.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184115-64649.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184115-88828.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184114-45630.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184115-64649.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184116-51613.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184114-70629.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184115-88828.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184116-85851.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184116-79717.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184117-34649.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184116-85851.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184117-49345.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184117-24026.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184117-34649.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184116-85851.gif)
(3)如果给定实系数基函数
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184114-45630.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184117-99731.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184117-47600.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184114-70629.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184117-15952.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184117-54600.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184116-79717.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184117-29104.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184117-24026.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184115-98702.gif)
A.3 | B.0 | C.-1 | D.-2 |
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184055-47479.gif)
(Ⅰ)写出函数
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184055-47479.gif)
(Ⅱ)求当x为多少时,容器的容积最大?并求出最大容积。
![](http://img.shitiku.com.cn/uploads/allimg/20200205/20200205184055-37725.gif)
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