Operations between functions: discover how to add two functions with explanations, definitions and practical examples to better understand this algebraic operation.
Mathematics is a discipline that deals with many topics, some of which may seem complex or boring, while others are more interesting because they are applicable to many situations in everyday life. When approaching this subject, the best way to overcome difficulties is to study one concept at a time, understanding each individual notion thoroughly.
Among the topics that we frequently encounter in mathematics lessons are functions . Functions are mathematical tools that allow us to associate each element of a starting set with a single element of a target set.
This guide will explore the addition of two functions , a fundamental concept in algebraic operations. Let’s see how to add two functions in a simple and clear way.
Function definition
To fully understand the sum of two functions, it is first necessary to clarify what a function is. A function is a relation between two sets , usually denoted by “A” and “B”, in which each element of the set A (called domain) corresponds to one and only one element in the set B (called codomain).
In other words, if f is a function, for every x ∈ A , there is a unique value f(x) ∈ B.
Once we understand what a function is, we can move on to the concept of the sum of two functions. The sum of two functions allows us to combine the values they assume for each point of their domain.
Definition of sum between functions
The sum of two real variable functions f(x) and g(x) is defined as: (f + g)(x) = f(x) + g(x) .
In order for this sum to be well defined, it is necessary that the domains of the two functions have a non-empty intersection . In other words, the domain of the sum (f + g)(x) will be the intersection of the domains of f(x) and g(x) , that is:
Dom(f + g) = Dom(f) ∩ Dom(g)
This means that the domain of the sum function will contain only the x’s that belong to both the domain of f(x) and that of g(x) .
