Given the function y = F & nbsp; (x) (x ∈ R, X ≠ 0), for any non-zero real number x1, X2, f (x1x2) = f (x1) + F (x2), try to judge the parity of F (x)

Given the function y = F & nbsp; (x) (x ∈ R, X ≠ 0), for any non-zero real number x1, X2, f (x1x2) = f (x1) + F (x2), try to judge the parity of F (x)

Let X1 = - 1 ·, X2 = x, F & nbsp; (- x) = F & nbsp; (- 1) + F & nbsp; (x) & nbsp ① In order to find the value of F & nbsp; (- 1), let X1 = 1, X2 = - 1, then f (- 1) = f (1) + F (- 1), that is, f (1) = 0, let X1 = x2 = - 1, then f (1) = f (- 1) + F (- 1) = 2F (- 1) = 0