Y = f (x) is defined in R, and its graph is symmetric with respect to the straight line x = A and x = B (a is not equal to b). It is proved that f (x) is a periodic function

Y = f (x) is defined in R, and its graph is symmetric with respect to the straight line x = A and x = B (a is not equal to b). It is proved that f (x) is a periodic function

Y = f (x) is defined in R, so we can take any x, and because the graph is symmetrical about the straight line x = a, f (x) = f (2a-x); its graph is symmetrical about x = B, so f (x) = f (2b-x); so f (2a-x) = f (2b-x), let t = 2a-x, then 2b-x = t + 2b-2a, that is, f (T) = f (T + 2b-2a), and because a is not equal to B, so 2b-2a is not equal to 0, so the period is 2b-2a, that is, y = f (x) is defined on R, and the period is 2b-2a
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