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Year 11 · Functions & Graphs
Inverse functions
Function notation f(x) means "the rule applied to x". f(3) is the rule with 3 put in.
How to do it
- Substitute the number for every x.
- Composite f(g(x)): work out g first, then put the result into f.
- Inverse: swap x and y, then make y the subject.
Worked example
f(x) = 6x + 0. Which is the inverse function f⁻¹(x)?
Swap x and y, then solve for y: x = 6y + 0 gives y = (x − 0) / 6.
Answer: (x − 0) / 6
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Watch outInside brackets first for composite functions.
Practise Inverse functions properly
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