Binary operation under which each pair (

*f*,*g*) of functions defined in a set E toward a set F, is made to correspond to a new function, noted as*f + g*, called the sum of these functions.To obtain the value of the sum of the two functions

*f*and*g*of variable*x*, simply add the images*f*(*x*) and*g*(*x*) : (*f*+*g*)(*x*) =*f(*x*) +*g*(*x*).*### Example

Consider these functions:

\(f_1 : \mathbb{R} → \mathbb{R} : x → f_1(x) = x\)

\(f_2 : \mathbb{R} → \mathbb{R} : x → f_2(x) = \sin{(x)}\)

On this graph, the orange line represents the sum of the functions represented in purple and yellow.

The sum of the functions \(f_1\) and \(f_2\) is defined as:

\(f_1 + f_2 : \mathbb{R} → \mathbb{R} : x → (f_1 + f_2)(x) = f_1(x) + f_2(x) = x + \sin (x)\)