A function gives exactly one output for each permitted input. In f(x)=3x-5, f names the rule and x is a placeholder. The notation f(4) means apply the rule to 4; it does not mean multiply f by 4. Example f(4)=3(4)-5=7, and f(t+2)=3(t+2)-5=3t+1. If f(x)=10, solve 3x-5=10, giving x=5. **Input** | **−1** | **0** | **2** Output under g(x)=x2 | 1 | 0 | 4 Different inputs may have the same output: g(-2)=g(2)=4. That does not stop g being a function. One permitted input producing two different outputs would fail the definition.

A function gives exactly one output for each permitted input. In \(f(x)=3x-5\), f names the rule and x is a placeholder. The notation \(f(4)\) means apply the rule to 4; it does not mean multiply f by 4.

\(f(4)=3(4)-5=7\), and \(f(t+2)=3(t+2)-5=3t+1\). If \(f(x)=10\), solve \(3x-5=10\), giving \(x=5\).

Different inputs may have the same output: \(g(-2)=g(2)=4\). That does not stop g being a function. One permitted input producing two different outputs would fail the definition.

Functions

Cambridge IGCSE Mathematics 0580. Initial catalogue covers the assessed demands of February/March 2026 Paper 22; further Core and Extended mappings require paper-level scope review.

Functions as input–output rules

Functions as input–output rules