Functions · Year 12
In Year 12 you learn: composite functions.
A function is a rule that turns each input into exactly one output, written like f(x) = 3x + 1. Function notation makes it easy to talk about combining rules (composite functions) and undoing them (inverse functions).
Key facts
- f(4) means substitute 4 into the function f.
- fg(x) means do g first, then f: fg(x) = f(g(x)).
Worked examples
Example 1
f(x) = 3x − 1 and g(x) = x² + 2. Find fg(2) and gf(x).
Answer: fg(2) = 17; gf(x) = 9x² − 6x + 3