Question

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．

Answer 1

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，