Composite Functions

MathematicsAQAEdexcelGCSEUnit: Algebra
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The basics

Chaining Functions Together

Chaining Functions Together

Imagine you have two machines: Machine G turns any number into double that number, and Machine F adds 3. If you want to double a number AND THEN add 3, you'd run it through G first, then F. This is called a COMPOSITE function - you chain the machines together to create a more complex process.
Composite functions diagram
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.
Key terms

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.
Spotlight
Key Facts

Key insight: fg(x) ≠ gf(x) in general! Order matters!

Exam tip

Earn the mark scheme marks

Common Mistakes to Avoid

✗ 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

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)

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