Grade 12 · Theory
Inverse functions
Functions and inverses · about 3 min
Visual overview: Inverse functionsThe inverse undoes the function, and its graph is the mirror image in the line y = x.
Key points- To find the inverse: swap x and y, then make y the subject.
- The graph of f⁻¹ is the reflection of f in the line y = x.
- Domain and range swap between a function and its inverse.
- A function has an inverse function only if it is one-to-one.
- Inverse — the function that reverses the original.
- One-to-one — each y comes from exactly one x.
EXAM TIP
the inverse of a parabola is not a function unless you restrict the domain — say which restriction you chose.