Who these notes are for
These free revision notes are for students taking Edexcel International A-Level Pure Mathematics 3 (P3, paper code WMA13). They focus on one topic area: functions, composite functions, inverse functions, and domain and range.
They are written for students who want a structured summary of this topic while revising for P3, and for anyone studying functions at A-Level who wants to strengthen the foundations.
What the notes cover
- Functions and function notation
- Composite functions
- Inverse functions
- Domain and range
The notes cover this one topic area of P3. They are not a complete P3 revision pack.
Key ideas at a glance
Functions and function notation
A function assigns exactly one output to each input in its domain. f(x) is the output when the function f is applied to the input x.
Composite functions
The composite function fg(x) means f(g(x)): apply g first, then apply f to the result. The order matters, and in general fg(x) is not the same as gf(x).
Inverse functions
The inverse function f⁻¹ reverses the effect of f. It exists only when f is one-to-one. The domain of f⁻¹ is the range of f, the range of f⁻¹ is the domain of f, and the graph of y = f⁻¹(x) is the reflection of y = f(x) in the line y = x.
Domain and range
The domain is the set of inputs a function is defined for. The range is the set of outputs it produces from that domain.
About the author
Dr Zhiying Xin is the founder of Study with Dr and a private Maths and Science tutor with nearly seven years of experience, teaching students from 11+ and GCSE through to A-Level and university. She completed her PhD at the University of Manchester.