This: f(x+a)=f(x+b), then T=a-b, the landlord should know.
1, if f(x+a)=-f(x), then T=2a.
2. If f(x+a)=m/f(x) and m≠0, then T=2a.
Ps: There is a rare one: f(x)=f(x- 1)-f(x-2), then T=6, and other periodic conclusions related to symmetry can be grasped.
Have fun! I hope I can help you ~ ~