top of page
Composite functions apply one function to the output of another, fg(x), while inverse functions f⁻¹(x) reverse a function. This topic covers forming composites, finding inverses, their domains and ranges and the reflection relationship. It's a key topic in A-Level and International A-Level (iAL) Pure Mathematics. This free interactive course teaches the method with worked examples and gives instant-feedback practice questions to lock it in.
How you do it
For fg(x), apply g first and put its output into f — the order runs right to left. For the inverse, write y equals f(x), swap x and y, and rearrange. The inverse only exists if the function is one-to-one, and its domain is the original range.
Before you start
The groundwork here is domain and range. This sits in Pure 3. It leads on to harder function questions. It is part of the Algebra strand.
What you learn
A composite function fg(x)=f(g(x)) applies g first, then f — order matters. An inverse f⁻¹ undoes f, and exists only when f is one-to-one. fg(x) means apply g first, then feed the result into f. To solve fg(x)=k, form the composite then solve. To find f⁻¹, write y=f(x), swap the roles of x and y, and make y the subject. The course works through forming composite functions, solving composite equations, finding the inverse, domain & range through inverses and composites and self-inverse functions & synthesis. Every section has instant-feedback practice questions matched to Edexcel International A-Level and 9MA0 Pure, and the course finishes with full exam-style questions you mark yourself.
Related Topics
In our A-level maths courses, Composite and Inverse Functions belongs to Algebra and is met in the AS year. There are 5 teaching sections and 5 fully worked examples, plus 5 sets of check questions. Related topics students usually take next include Factor & Remainder Theorem, Functions - Domain and Range, Improper Algebraic Fractions and Indices and Surds. For unlimited practice, the Algebra revision engine builds new questions on demand and records your accuracy.
Still need help with a topic?
bottom of page