bartyp
幼苗
共回答了18个问题采纳率:94.4% 举报
对于函数
![](https://img.yulucn.com/upload/2/cd/2cd7f7cd14098eb4dc2676d3899510c0_thumb.jpg)
,有下列五个命题:
①若
![](https://img.yulucn.com/upload/2/cd/2cd7f7cd14098eb4dc2676d3899510c0_thumb.jpg)
存在反函数,且与反函数图象有公共点,则公共点一定在直线
![](https://img.yulucn.com/upload/1/ef/1ef4edaf9b2b1f42c0e607b04b7f9e72_thumb.jpg)
上;
②若
![](https://img.yulucn.com/upload/2/cd/2cd7f7cd14098eb4dc2676d3899510c0_thumb.jpg)
在
![](https://img.yulucn.com/upload/e/2f/e2f7da9a27c308f3722b1df240f8dbfe_thumb.jpg)
上有定义,则
![](https://img.yulucn.com/upload/3/de/3de82461f838293d6176b23fbbe5fc3b_thumb.jpg)
一定是偶函数;
③若
![](https://img.yulucn.com/upload/2/cd/2cd7f7cd14098eb4dc2676d3899510c0_thumb.jpg)
是偶函数,且
![](https://img.yulucn.com/upload/2/28/22895d96616f5413bf2bf35efd1615e3_thumb.jpg)
有解,则解的个数一定是偶数;
④若
![](https://img.yulucn.com/upload/0/c6/0c66b0c67f04b7339d5a121f936a2c0b_thumb.jpg)
是函数
![](https://img.yulucn.com/upload/2/cd/2cd7f7cd14098eb4dc2676d3899510c0_thumb.jpg)
的周期,则
![](https://img.yulucn.com/upload/0/64/064ff46786de9bf5c186eb2a2d869e13_thumb.jpg)
,也是函数
![](https://img.yulucn.com/upload/2/cd/2cd7f7cd14098eb4dc2676d3899510c0_thumb.jpg)
的周期;
⑤
![](https://img.yulucn.com/upload/6/2d/62d6c76af5e72256e68288d307308421_thumb.jpg)
是函数
![](https://img.yulucn.com/upload/2/cd/2cd7f7cd14098eb4dc2676d3899510c0_thumb.jpg)
为奇函数的充分不必要条件。
从中任意抽取一个,恰好是真命题的概率为 ()
A.
![](https://img.yulucn.com/upload/e/23/e2356574e4bac65f065b81c0136b0a4c_thumb.jpg)
B.
![](https://img.yulucn.com/upload/7/76/776be861d9c6b197d2b72af6a3c6091a_thumb.jpg)
C.
![](https://img.yulucn.com/upload/5/31/531dc5c8cad85bbc573531a0e995fa01_thumb.jpg)
D.
B
①若y=f(x)存在反函数,且与反函数图象有公共点,则公共点不一定在直线y=x上,如函数f(x)=
![](https://img.yulucn.com/upload/b/12/b1260a746d07e7f1d1ea0e77fd086fe9_thumb.jpg)
,反函数是其本身,公共点是整个函数图象;
②若y=f(x)在R上有定义,则y=f(|x|)一定是偶函数,因f(|-x|)=f(|x|)对于任意x恒成立,故正确;
③若y=f(x)是偶函数,且f(x)=0有解,则解的个数一定是偶数不正确,如y=x
2 ,是偶函数,x
2 =0的解只有一个,不是偶数个;
④若T(T≠0)是函数y=f(x)的周期,则f(x+T)=f(x),从而f(x+nT)=f(x),则nT(n∈N),也是函数y=f(x)的周期;
⑤f(0)=0是函数y=f(x)为奇函数的充分也不必要条件,不正确,f(x)=x
2 时,f(0)=0,而f(x)=x
2 是偶函数.
故正确的命题有2个,
则从中任意抽取一个,恰好是真命题的概率为
故选B.
1年前
3