Adding Functions

Adding Functions

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).


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:

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

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