Which of the following equations are true for all operators A and B and all functions f

Question:

Which of the following equations are true for all operators A and B and all functions f and g?
(a) (A+ B)f = Af + Bf;
(b) A(f + g) = Af + Ag ;
(c) (Af)/f = A, provided f ≠ 0;
(d) AB f = BAf;
(e) Af = fA;
(f) (Bf)g = B(fg);
(g) B(fg) = B(gf);
(h) (Bg)f = f(Bg).