# Theory of Equations/Functional Equations

Welcome to the Lesson of Functional Equations
Part of the School of Olympiads

In mathematics or its applications, a functional equation is an equation expressing a relation between the value of a function (or functions) at a point with its values at other points. Properties of functions can for instance be determined by considering the types of functional equations they satisfy. The term functional equation is usually reserved for equations that are not in a simple sense reducible to algebraic equations, often because two or more known functions are substituted as arguments into another function.

## Examples

```3(x-2)=x+2
= 3x-6=x+2
= 3x-x-6=2
= 3x-x=2+6
= 2x=8
= 2x÷2=8÷2
```

## Active participants

The histories of Wikiversity pages indicate who the active participants are. If you are an active participant in this division, you can list your name here (this can help small divisions grow and the participants communicate better; for large divisions a list of active participants is not needed).