P3.1.2 - Definition of a function

Definition of a function.; Domain The concept of a function as a one-one or many-one and range of functions. mapping from (or a subset of) to.; The notation Composition of functions.; Inverse f: x and f(x) will be used. functions and their graphs. ℝ ℝ ℝ Students should know that fg will mean ‘do g first, then f ’.; Students should know that if f −1 exists, then f −1f(x) = ff −1(x) = x.

Use definition of a function to connect the rule to the data and decision in the question.

This matters because definition of a function determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply definition of a function to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Definition of a function is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.