题目内容
(本题满分10分)已知函数
的定义域为
,对定义域内
的任意
、
,都有
=
, 且当
时,
.
(1)求
、
的值;(4分)(2)求证:
在
上是增函数. (6分)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155408582270.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155408613598.gif)
的任意
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155408629198.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155408660203.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155408676334.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155408691418.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155408723230.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155408738328.gif)
(1)求
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155408754266.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155408785279.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155408582270.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155408816410.gif)
(1)
=0,
=0
(2)
在
上是增函数.证明略。
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155408754266.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155408785279.gif)
(2)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155408582270.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155408816410.gif)
解:(1)令
=
="1,"
=2
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409050128.gif)
=0![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
(2分)
令
=
,
=2
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409050128.gif)
=0![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
(2分)
(2)设
,则
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409752536.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
(2分)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231554103141074.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
(2分)
即
在
上是增函数. ![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
(2分)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155408629198.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155408660203.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409019469.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155408754266.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409050128.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155408754266.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
令
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155408629198.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409191251.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409206493.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155408785279.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409050128.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155408785279.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
(2)设
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409705422.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409721307.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409752536.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/201408231554103141074.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
即
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155410891413.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155410938284.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155408816410.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/pic2/upload/papers/20140823/20140823155409081177.gif)
![](http://thumb.zyjl.cn/images/loading.gif)
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