题目

题型：解答题难度：一般来源：不详

函数的定义域为，并满足条件
①对任意，有；
②对任意，有；
③．
（1）求的值；
（2）求证：在上是单调递增函数；
（3）若，且，求证．

答案

1

解析

解法一：（1）令，则                                                                  
                                                                                                              
（2）任取，且
设，则
                                      ，                                                                  ，在上是单调递增函数                                                      
（3）由（1）（2）知，                                                              
                                                                                        
又，                                                                                                                                         
解法二：（1）对任意，有
                                                                                                       
当时，                                                                                               ，，                                                                                    
（2），                                                             
是上的单调增函数
在上是单调递增函数                                                                                              
（3）                                                                
而，