There is a non-zero constant t, which holds true for x in any domain.

1)f(x t)=f(x)

2)f(x+t)=f(x)

Then f(x) is said to be a periodic function and t is one of its periods.

If 1) is adopted, the domain of the periodic function must be unbounded at both ends, and if 2) is adopted, only one end is needed.

Strictly follow the textbook, if there is no clear definition in the textbook, I imagine that the college entrance examination will avoid such problems.

Because this definition is to find a mathematical definition that can reflect this law in mathematics after observing the actual things or phenomena, it is hard to say which definition is more in line with people's original intention. I don't think anything is wrong or correct.

In addition, "Baidu Encyclopedia says that the domain M of the periodic function f(x) must be an unbounded set on both sides. What he means is that the "unbounded on both sides" in the real number set R is not necessarily a real number set, such as y=tanx.