Functions

What is Functions?

A rule that assigns to each input in its domain exactly one output, the set of outputs actually produced being its range. Function notation writes the output of f at x as f of x. The inverse function reverses a one-to-one function, so that if f maps four to seven then its inverse maps seven to four, and it is found by swapping x and y and making y the subject. A composite function applies two functions in succession, and Cambridge writes gf of x to mean g of f of x, so the function written nearest to x acts first.

This definition is part of the Algebra and Graphs chapter in Cambridge O Level Mathematics (Syllabus D).

Concepts related to Functions

• domain
• range
• mapping diagram
• inverse function
• composite function
• one-to-one