Basics

In mathematics, a function is written as a map that uniquely assigns an element y from the range R to every element x from the domain D.

This is expressed by f : D → R

Alternatively, when considering particular elements x and y, one writes f : x → y

Here, f is called the name of the function and f(x) is its value when applied to x. Here, x is sometimes called the argument of f. Let's first look at an example before considering functions in Python.

For example, D = ℝ x ℝ  and y = f(x₁, x₂) = x₁ - x₂ . This function maps two real numbers to their difference.

In mathematics, functions can have numbers, vectors, matrices, and even other functions as arguments. Here is an example of a function with mixed arguments: 

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In this case, a number is returned. When working with functions, we have to distinguish between two different steps:

• The definition of the function
• The evaluation of the function, that is, the computation of f(x) for a given value of x

The first step is done once, while the second...