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Paper 3
Functions & Graphs
Higher
Functions map inputs to outputs.
Key Facts
- Composite functions combine two rules.
- Inverse functions undo each other.
Topics Covered
Function Notation
What you need to know
- •f(x) is the output when you input x.
- •Composite functions apply one after another.
Exam Tips
- Write the inside function first.
Inverse Functions
What you need to know
- •Swap x and y then solve for y.
- •Check f(f^-1(x)) = x.
Exam Tips
- State domain restrictions if needed.
Key Terms
Composite
A function applied to another function.
Inverse
A function that undoes another function.
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Common Exam Questions
If f(x) = 2x + 3, find f^-1(x).
3 marksmediumPaper 3
Model Answer
(x - 3) / 2
What examiners want to see
- ✓Swap x and y then solve.
Let g(x) = x^2. Find g(f(4)) for f(x) = x - 1.
2 markseasyPaper 3
Model Answer
9
What examiners want to see
- ✓Apply f then g.
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