【题文】设函数(x∈R)为奇函数,=,,则=( )A.0B.1 C.D.5
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【题文】设函数
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326223045-38086.png)
(x∈R)为奇函数,
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326223045-11052.png)
=
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326223045-59799.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326223045-27584.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326223045-24822.png)
=( )
A.0 | B.1 | C.![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326223046-85605.png) | D.5 |
答案
【答案】C
解析
【解析】解:因为函数y=f(x)为奇函数且f(1)=1/2,则f(1)=f(-1)+f(2),所以f(2)=2f(1)=1,
又因为f(3)="f(1)+f(2)=3/2," f(5)=f(3)+f(2)=5/2,选C
举一反三
【题文】设函数
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326223029-37450.png)
(x∈R)为奇函数,
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326223029-64875.png)
=
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326223030-70485.png)
,
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326223030-24969.png)
,则
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326223030-11568.png)
=( )
A.0 | B.1 | C.![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326223031-73716.png) | D.5 |
【题文】设函数
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326223022-89222.png)
为定义在R上的奇函数,当
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326223023-33046.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326223023-85200.png)
(
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326223023-34564.png)
为常数),则
;
【题文】设函数
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326222816-35103.png)
为定义在R上的奇函数,当
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326222817-24424.png)
时,
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326222817-16414.png)
(
![](http://img.shitiku.com.cn/uploads/allimg/20200326/20200326222818-50659.png)
为常数),则
;
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