有下列4个命题：

①若函数f（x）定义域为R，则g（x）=f（x）﹣f（﹣x）是奇函数；

②若函数f（x）是定义在R上的奇函数，∀x∈R，f（x）+f（2﹣x）=0，则f（x图象关于x=1对称；

③已知x₁和x₂是函数定义域内的两个值（x₁＜x₂），若f（x₁）＞f（x₂），则f（x）在定义域内单调递减；

④若f（x）是定义在R上的奇函数，f（x+2）也是奇函数，则f（x）是以4为周期的周期函数．

其中，正确命题是____ （把所有正确结论的序号都填上）．

根据短文内容选择正确答案。

    Mrs. Smith is Jim's mother. She loves her family very much.  She goes to the store every day. She often buys food, fruit and clothes for Jim and her husband. Now many clothes are on sale at Renmin Clothes Store. They are very cheap. Mrs. Smith comes to the store and she wants to buy some clothes for her family. There they have sweaters in all colors for ￥15 each and sports shoes for only ￥28. Mrs. Smith likes the red sweater and she buys one for herself. She buys a pair of sports shoes for her son. The great T-shirts in the store are just ￥18!  She buys a white one for Mr. Smith. And that's not all. The socks, in all colors, are ￥2 each. She buys the socks in many colors for her family. She is really a Rood mother and a good wife (妻子).