✗ Getting the order wrong
✓ fg(x) means do g first, then f
The function closest to x is done first
✗ Thinking fg(x) = gf(x)
✓ Order usually matters - they're different
Different order gives different results
✗ Confusing fg(x) with f(x) × g(x)
✓ Composite means "function of function"
It's substitution, not multiplication
This exam tips covers Common Mistakes to Avoid within Composite Functions for GCSE Mathematics. Revise Composite Functions in Algebra for GCSE Mathematics with 14 exam-style questions and 12 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 7 of 8 in this topic. Treat this as a marking guide for what examiners are looking for, not just a fact list.
Practice questions for Composite Functions
The composite function fg(x) means: A) Apply g first, then apply f to the result B) Apply f first, then apply g to the result C) Multiply f(x) by g(x) D) Add f(x) to g(x)
Explain why, in general, fg(x) and gf(x) are NOT equal. You may use an example to support your explanation.
Quick recall flashcards
What does fg(x) mean?
fg(x) = f(g(x)): apply g first (inner function), then apply f to the result.
Do the function closest to x first.
What is a composite function?
A function formed by chaining two functions together.
The output of one function becomes the input of the next.