Functions · Grade 12
In Grade 12 you get fluent with: 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.
- The domain is the set of allowed inputs; the range is the set of outputs.
- 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.
- Leave out of the domain any x that makes you divide by 0 or take the square root of a negative.
Worked examples
Example 1
Find the inverse of f(x) = (2x + 5)/3.
Answer: f⁻¹(x) = (3x − 5)/2
Example 2
Give the domain and range of f(x) = √(x − 4).
Answer: Domain x ≥ 4; range f(x) ≥ 0