Question

函數的定義域為，并滿足條件
①對任意，有；
②對任意，有；
③．
（1）求的值；
（2）求證：在上是單調遞增函數；
（3）若，且，求證．

Answer 1

1

解法一：（1）令，則                                                                  
                                                                                                              
（2）任取，且
設，則
                                      ，                                                                  ，在上是單調遞增函數                                                      
（3）由（1）（2）知，                                                              
                                                                                        
又，                                                                                                                                         
解法二：（1）對任意，有
                                                                                                       
當時，                                                                                               ，，                                                                                    
（2），                                                             
是上的單調增函數
在上是單調遞增函數                                                                                              
（3）                                                                
而，