SL 2.2—Functions and inverses
- Syllabus
- First assessment 2021
- Objective
- —
- Level
- HL
An inverse undoes a function on the right domain
The inverse function f⁻¹ reverses the mapping: f⁻¹(f(x))=x and f(f⁻¹(x))=x on their appropriate domains. A function needs to be one-to-one for an inverse function to exist without restricting the domain.
To find an inverse, write y=f(x), interchange x and y, then solve for y. Graphically, f and f⁻¹ reflect in y=x, so the domain and range swap.
For f(x)=2x+3, y=2x+3 gives x=(y−3)/2, so f⁻¹(x)=(x−3)/2. A quadratic needs a domain restriction before its inverse is a function.
f⁻¹(x) is not 1/f(x). Always check composition and state the domain restriction when the original graph fails the horizontal-line test.