Functions · Grade 12
In Grade 12 you learn: inverse functions; domain and range.
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)).
- The inverse f⁻¹(x) undoes f. Write y = f(x), swap x and y, and make y the subject.
- Only one-to-one functions have an inverse; the graph of f⁻¹ is the reflection of the graph of f in y = 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
Example 2
Find the inverse of f(x) = (2x + 5)/3.
Answer: f⁻¹(x) = (3x − 5)/2