A Shortcut for the Inverse — Cheat sheet

Key method

If $f=g\circ h$ and both maps are bijective between their specified sets, then

The last operation performed is the first operation undone.

Example

For $f(x)=2(x-3)^3+5$, first subtract $3$, cube, multiply by $2$, then add $5$. Reverse these operations: subtract $5$, divide by $2$, take a cube root, add $3$.

Cube roots are single-valued over the reals, so no branch restriction is needed.

Avoid this mistake

Undoing in the same order is wrong. Squaring also requires a domain restriction before a square root can undo it.