(1)猜想:
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122930503590.gif)
或
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122930596590.gif)
;---------------------4分
由
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122930503590.gif)
知
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122930737800.gif)
,而
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122930752506.gif)
为奇函数且在
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122930331507.gif)
上是增函数。--------------------------------------6分
由
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122930596590.gif)
知
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122930815854.gif)
,而
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122930861532.gif)
为奇函数且在
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122930331507.gif)
上是增函数。----------------------------8分
(2)由
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122930893270.gif)
为奇函数,有
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408231229309551039.gif)
所以
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122930971571.gif)
,又
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122930986716.gif)
,
解得
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122931002606.gif)
。--------------------------------------------------10分
当
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122931017514.gif)
时,
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408231229310331024.gif)
为奇函数,由于
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122930893270.gif)
在
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122931064437.gif)
上是增函数,所以
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122931095260.gif)
,由
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122931251811.gif)
,又
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122930893270.gif)
在
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122931064437.gif)
上是增函数,故有
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408231229312981140.gif)
,且
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122931314350.gif)
或
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122931329197.gif)
,故
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122930659904.gif)
。-------------------------12分
当
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122931361598.gif)
时,
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408231229313761105.gif)
为奇函数,由于
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122930893270.gif)
在
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122931064437.gif)
上是增函数,所以
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122931470261.gif)
,由
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122931548823.gif)
,又
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122930893270.gif)
在
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122931064437.gif)
上是增函数,故有
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408231229315951145.gif)
,且
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122931719346.gif)
或2,故
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408231229306741000.gif)
--------------------------------------14分
所以所有符合题意的
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122930393201.gif)
与
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122930409205.gif)
的值为:
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/20140823122930659904.gif)
或
![](http://thumb.1010pic.com/pic2/upload/papers/20140823/201408231229306741000.gif)
-------------------------16分