The image of the function FX defined on R is symmetric with respect to the point a (a, b) B (C, b), and the period of the function is calculated

The image of the function FX defined on R is symmetric with respect to the point a (a, b) B (C, b), and the period of the function is calculated

∵ function y = f (x) the image is centrosymmetric with respect to point a (a, b),
∴f (x) + f (2a－x) =2b,……………… （1）
And ∵ function y = f (x) image B (C, b) symmetry,
∴f (x) + f (2c－x) =2b,
Substituting 2a-x for X, we get the following results
f (2a－x) + f [2c－(2a－x) ] =2b……………… （2）
By comparing (1) and (2), we can see that f [2C - (2a-x)] = f (x)
That is, f [x + 2 (C-A)] = f (x)
So the function is periodic and the period is 2 | C-A |