题目
题型:难度:来源:
【题文】定义在R上的函数
满足
,
,
,且当
,时,
.
(1)
;(2)
.
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014341-19864.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014342-65753.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014342-83005.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014342-13874.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014342-83807.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014342-60797.png)
(1)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014343-57180.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014343-14885.png)
答案
【答案】(1)
(2)![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014343-19475.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014343-44378.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014343-19475.png)
解析
【解析】
试题分析:当x=0时,f(0)+f(1-0)=1,得f(1)=1;
当x=
时,
得f(
)=
;
由f
得f(
)=
f(1)=
;f(
)=
f(
)=
;f(
)=
f(
)=
;f(
)=
f(
)=
;f(
)=
f(
)=
.
由f
得f(
)=
f(
)=
;f(
)=
f(
)=
;f(
)=
f(
)=
;
f(
)=
f(
)=
;
又因为
,时,
.
所以f(
)
f(
)
而f(
)=f(
)=
且函数在(0,1)上是单调增函数,所以![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014343-14885.png)
,
1- f(
)=1-
=
.
考点:1.抽象函数;2.函数的单调性.
试题分析:当x=0时,f(0)+f(1-0)=1,得f(1)=1;
当x=
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014344-39141.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014344-14686.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014344-39141.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014344-39141.png)
由f
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014342-13874.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014345-70345.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014344-39141.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014344-39141.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014345-90005.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014344-39141.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014345-70345.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014345-38113.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014345-50267.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014344-39141.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014345-70345.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014345-10480.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014346-10062.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014344-39141.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014345-50267.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014346-23532.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014346-25111.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014344-39141.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014346-10062.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014343-19475.png)
由f
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014342-13874.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014346-92002.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014344-39141.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014344-39141.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014345-38113.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014347-12834.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014344-39141.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014346-92002.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014345-10480.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014347-20960.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014344-39141.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014347-12834.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014346-23532.png)
f(
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014347-42129.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014344-39141.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014347-20960.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014343-19475.png)
又因为
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014342-83807.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014342-60797.png)
所以f(
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014346-25111.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014347-55783.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014347-42129.png)
而f(
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014346-25111.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014347-42129.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014343-19475.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014343-14885.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014343-19475.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014343-57180.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014345-90005.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014345-38113.png)
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014343-44378.png)
考点:1.抽象函数;2.函数的单调性.
核心考点
举一反三
【题文】函数
的增区间为 .
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326014316-65292.png)
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