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In high school mathematics, isn't the symmetry axis of even-numbered functions x=0 (that is, axis symmetry about Y), but why does the following question say that the symmetry axis is x= 1?
Even functional symmetry about x=0 does not affect that x= 1 is symmetric (there can be more than one axis of symmetry).

So f(x)=f(2-x), and the symmetry axis is: x = (x+2-x)/2 =1;

Expand:

Similar to abstract function problem:

F(x+2)=-f(x): the period is 4.

F(x)=f(x+2): the period is 2.

……

There are many such problems. Practice more.