It is known that f (AB) = f (a) + F (b) holds for any real number a and B 1) Finding the value of F (1) and f (0) 2) If f (2) = P, f (3) = q (P, q are constant), find the value of F (36) 3) Prove f (1 / x) = - f (x)

It is known that f (AB) = f (a) + F (b) holds for any real number a and B 1) Finding the value of F (1) and f (0) 2) If f (2) = P, f (3) = q (P, q are constant), find the value of F (36) 3) Prove f (1 / x) = - f (x)

（1）
Let a = b = 1
f(1×1)=f(1)+f(1)
f(1)=f(1)+f(1)
So f (1) = 0
Let a = b = 0
f(0×0)=f(0)+f(0)
f(0)=f(0)+f(0)
So f (0) = 0
（2）
f(36)
=f(2×18)
=f(2)+f(18)
=p+f(2×9)
=p+f(2)+f(9)
=p+p+f(3×3)
=p+p+f(3)+f(3)
=p+p+q+q
=2(p+q)
(3)
Let a = x, B = 1 / x, then 0 = f (1) = f (x) + F (1 / x)
That is f (1 / x) = - f (x)