Function

• Definition: A function is a special type of Relation that assigns each element of a domain $A$ to exactly one element of a codomain $B$.
• Notation: $f:A\to B$ where $f(x)\in B$ for every $x\in A$
• Key Parts:
  • Domain of a Function
  • Codomain of a Function
  • Image of a Function
• Important Rule: Each input has exactly one output, but different inputs may share the same output.
• Example:
  • $f(x)=x^2:\mathbb{R}\to \mathbb{R}$
  • Domain = $\mathbb{R}$
  • Codomain = $\mathbb{R}$
  • Image = $[0,\infty )$