Pass Check: Functions
Use function notation to substitute, combine and reverse functions.
Function
A rule that takes an input x and produces exactly one output, written f(x).
Composite function
Applying one function to the result of another, written fg(x), meaning f(g(x)).
Inverse function
A function that reverses another function, written f⁻¹(x), undoing what f(x) does.
Domain and range
The domain is the set of possible inputs; the range is the set of possible outputs.
Quick check
Mixed quiz
1. Which of these is correct function notation?
2. Which expression represents ff(x) if f(x) = x + 2?
3. For f(x) = x², why must the domain be restricted (e.g. x ≥ 0) to have an inverse?
4. Which expression equals x/2 × 4/x?
5. Which fraction is equivalent to 5x/10x?
6. Which formula describes 'add 3 to the previous term'?
7. For x³-x-3=0, if f(1.65)=0.106 (positive), what does this tell us about the root to 2dp, given f(1.5)<0?
8. Which pair of values would you test next to narrow down a root known to be between 2 and 3?