GCSE & A-level Introduction to Composite Functions (Part 2)

In this video, Lee Guffick (former Head of Maths and current A-Level Examiner) continues his explanation of composite functions for both GCSE and A-Level Maths. This is Part 2 in the series, where Lee takes things further by exploring functions within functions within functions — triple composite functions. He works through both numerical and algebraic examples, showing how to carefully build solutions step-by-step from the inside out. By the end of this lesson, you’ll understand how to evaluate and simplify even the trickiest composite functions, setting you up for success in exams. ⏱️ TIMESTAMPS: 00:00 – Introduction (composite functions recap) 00:40 – Triple composite functions explained (f(x), g(x), h(x)) 01:50 – Worked example: h(g(f(–1))) = 49 03:40 – Moving from numerical to algebraic examples 04:10 – Worked algebraic example: h(g(f(x))) 05:30 – Simplifying roots and fractions step-by-step 06:30 – When to leave answers vs. simplify further 07:00 – What’s next: inverse functions, domain & range ✏️ TOPICS COVERED: Recap of composite functions (inner and outer) Triple composites: h(g(f(x))) Step-by-step numerical example (substitution) Full algebraic worked example Simplifying surds and fractions Exam-style reasoning and presentation 💯 EXAM TIPS: Always work from the inside out Clearly identify inner, middle, and outer functions Be confident moving between numbers and algebra Triple composites can look scary, but they follow the same simple rule 📚 ABOUT GUFFICK TUITION: Lee Guffick is a premium online maths tutor, former Head of Mathematics, and current A-Level Examiner. His students consistently achieve top grades (A*/A) and progress to elite universities including Oxford, Cambridge, and Ivy League institutions. 📅 JOIN OUR PROGRAMME: → Personalised 1:1 tutoring: https://www.gufficktuition.com/tutoring → Small group classes: https://www.gufficktuition.com/group-... → Summer intensive courses: https://www.gufficktuition.com/tutoring 📱 CONNECT WITH US: → Instagram: @leeguffick → Website: https://www.gufficktuition.com → Email: [email protected] #GCSEMaths #ALevelMaths #CompositeFunctions #MathsTutor #GuffickTuition #ExamTips