Prove that an Anti-Periodic Function is Periodic

Prove that an Anti-Periodic Function is Periodic

[angelmendez-rivera]

If f(x + a) = –f(x) for all x in dom(f), then f(x + 2·a) = f(x + (a + a)) = f((x + a) + a) = –f(x + a) = (–1)^2·f(x) = 1·f(x) = f(x) for all x in dom(f).