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:
[latex]f_1 : \mathbb{R} → \mathbb{R} : x → f_1(x) = x[/latex]
[latex]f_2 : \mathbb{R} → \mathbb{R} : x → f_2(x) = \sin{(x)}[/latex]
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On this graph, the orange line represents the sum of the functions represented in purple and yellow.
The sum of the functions [latex]f_1[/latex] and [latex]f_2[/latex] is defined as:
[latex]f_1 + f_2 : \mathbb{R} → \mathbb{R} : x → (f_1 + f_2)(x) = f_1(x) + f_2(x) = x + \sin (x)[/latex]
