A functions whose range is a subset of the set of real numbers is called a real valued function. Two real valued functions f and g can be combined to form new functions f + g, f − g, fg, and 

in a manner similar to the way we add, subtract, multiply and divide real numbers. These are formally defined next.

Definition

Suppose f and g are two real valued functions. Let S = dom (f) ∩ dom (g).

(i) Sum of functions: The sum of f and g, f + g, is a function given by
(f + g)(x) = f (x) + g(x), for every x∈ S.

(ii) Difference of functions: The difference of f and g, f - g, is a function given by
(f - g)(x) = f (x) - g(x), for each x ∈S.

(iii) Product of functions: The product of f and g, fg, is a function given by
(f g)(x) = f (x)g(x), for each x ∈ S. (Here, f (x)g(x) = f (x) × g(x).)

(iv) Quotient of functions: The quotient of f and g,

is a function given by