Function

A function is a special type of Relation that assigns each element of a domain $A$ to exactly one element of a codomain $B$.

In human terms, a function from a set $A$ to another set $B$ is a (deterministic) rule that, given an element of $A$ as input, provides an element of $B$ as an output.

Notation

$$f:A\to B$$

where $f(x)\in B$ for every $x\in A$

Key Properties

• Domain of a Function
• Codomain of a Function
• Image of a Function

Examples

• $f(x)=x^2:\mathbb{R}\to \mathbb{R}$
• Domain = $\mathbb{R}$
• Codomain = $\mathbb{R}$
• Image = $[0,\infty )$