Combining & Undoing

Composition and inverse functions

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Composition $f(g(x))$: apply $g$ first, then $f$; order matters.
• An inverse undoes a function; its graph is the reflection in $y = x$.
• Only one-to-one functions have inverses (horizontal line test).

Steps

1. Machines in a row
2. Inside out
3. Undo buttons
4. Reflect a point
5. Not always undoable
6. Undo the temperature