题目内容
对于函数
,若存在实数对(
),使得等式
对定义域中的每一个
都成立,则称函数
是“(
)型函数”.
(1) 判断函数
是否为“(
)型函数”,并说明理由;
(2) 若函数
是“(
)型函数”,求出满足条件的一组实数对
;
(3)已知函数
是“(
)型函数”,对应的实数对
为(1,4).当
时,![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613023555.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613039611.png)
,若当
时,都有
,试求
的取值范围.
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031612805447.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031612820401.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031612836759.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031612852266.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031612805447.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031612820401.png)
(1) 判断函数
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031612898521.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031612820401.png)
(2) 若函数
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031612930620.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031612820401.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031612945480.png)
(3)已知函数
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031612976442.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031612820401.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031612945480.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613008491.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613023555.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613039611.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613054538.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613070537.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613086618.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613101337.png)
(1)
不是“(
)型函数”,理由详见解析;(2)
(答案不唯一)(3)![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613164539.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031612898521.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031612820401.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613148471.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613164539.png)
试题分析:(Ⅰ) 由给出的定义可知
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031612836759.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031612805447.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031612820401.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031612805447.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031612820401.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613257500.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613288783.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613304586.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613008491.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240316133351093.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613351545.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613008491.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031612976442.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613398536.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613257500.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031612976442.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613070537.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031612976442.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613086618.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031612976442.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613507360.png)
试题解析:解: (1)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031612898521.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031612820401.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031612945480.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613569684.png)
即
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613585532.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031612852266.png)
(2) 由
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613616578.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613616475.png)
如
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613632549.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613647792.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613663433.png)
(3)由题意得,
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613678684.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613257500.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613288783.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613304586.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613008491.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240316137561038.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613351545.png)
当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613772538.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613788460.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031612976442.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613819361.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613834588.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613850518.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031612976442.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613881418.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613897999.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613912740.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613928539.png)
当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613944642.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613959511.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031612976442.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613990800.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031614006709.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031612976442.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613881418.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240316141461211.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031614162994.png)
且
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240316141621065.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613959511.png)
当
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031614193671.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031614209507.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031612976442.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031614240782.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031614256723.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031612976442.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613881418.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240316142871197.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031614318952.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/201408240316143341115.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031614209507.png)
综上所述,所求
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613101337.png)
![](http://thumb.1010pic.com/pic2/upload/papers/20140824/20140824031613164539.png)
![](http://thumb2018.1010pic.com/images/loading.gif)
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