If f and g are real valued functions of x with domain set A and B respectively, then both f and g are defined in A ∩ B. Then,
(a) (f + g) x = f (x) + g(x) : Domain A ∩ B
(b) (f – g) x = f (x) – g(x) : Domain A ∩ B
(c) (fg) x = f (x) . g(x) : Domain A ∩ B
(d) \(\big[\frac{f}{g}\big]x = \frac{f(x)}{g(x)}\) : Domain A ∩ B
(e) (f + k) x = f (x) + k : k is constant, so domain = A
(f) (kf ) x = k f (x)
(g) f n(x) = [f (x)]n
