Question

函數(shù)的定義域為，并滿足條件

① 對任意，有；

② 對任意，有；

③ ．

（1）求的值；

（2）求證：在上是單調(diào)遞增函數(shù)；

（3）若，且，求證．

Answer 1

1

解析:

解法一：（1）令，則                                                                  

                                                                                                               

（2）任取，且

設(shè)，則

                                       ，                                                                           ，在上是單調(diào)遞增函數(shù)                                                       

（3）由（1）（2）知，                                                              

                                                                                         

         又，                                                                                                                                           

解法二：（1）對任意，有

                                                                                                       

當時，                                                                                                ，，                                                                                     

（2），                                                             

是上的單調(diào)增函數(shù)

在上是單調(diào)遞增函數(shù)                                                                                              

（3）                                                                

而，