Chaining Functions Together
Chaining Functions Together
Mathematics glossary
- 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.
Key insight: fg(x) ≠ gf(x) in general! Order matters!
Earn the mark scheme marks
Common Mistakes to Avoid
Now try it yourself
Quiz · Question 1 of 14
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)
Tap an answer to check it
This topic in real past papers
Every real exam question we've found on composite functions, with a full worked answer.
AQA Paper 2
Three of the four sittings we have full papers for require finding an inverse function, or combining a function with a composite or its inverse.
AQA Paper 3
Three of the four sittings we have full papers for combine two functions given in function notation, then use the result to solve an equation or identify the correct composite expression.
Edexcel Paper 1
Two of the three sittings we have full papers for build a question around inverse and composite functions together, one proving a quadratic equation and one solving for a specific value.