It is known that the function f (x) is defined on R, for any x, y belongs to R, f (x + y) + F (X-Y) = 2F (x) f (y), and f (0) is not equal to 0 1, prove that f (0) = 1.2, y = f (x) is even function

It is known that the function f (x) is defined on R, for any x, y belongs to R, f (x + y) + F (X-Y) = 2F (x) f (y), and f (0) is not equal to 0 1, prove that f (0) = 1.2, y = f (x) is even function

Let x, y = 0
We get 2F (0) = 2F (0) f (0)
Because f (0) is not equal to 0, f (0) = 1