For functions f: X → R and g: X → R, we have (f + g)(x) = f(x) + g(x), x ∈ X (f - g)(x) = f(x) - g(x), x ∈ X (fg)(x) = f(x) . g(x), x ∈ X (kf)(x) = k (f(x)), x ∈ X, where k is a real number. (f/g)(x) = f(x) / g(x), x ∈ X, g(x) ≠ 0