Algebra · Functions
Chapter 1 · 4
The idea
Inverse functions
Why f⁻¹ runs the machine backwards (and is NOT 1/f), the write-swap- rearrange recipe for finding it, and the ff⁻¹(x) = x check that catches every error.
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Algebra · Functions
Inverse functions
Why f⁻¹ runs the machine backwards (and is NOT 1/f), the write-swap- rearrange recipe for finding it, and the ff⁻¹(x) = x check that catches every error.
Why it works
The machine, run backwards
"Find " — and the notation immediately sets a trap, because looks like a power, and is the classic wrong answer. The is not a power; it is the undo badge. The inverse function runs the machine backwards: if turns into , then turns back into . Our machine for the lesson is the familiar .The recipe: write, undo, relabel
Finding the inverse is three moves, and the middle one is pure rearranging:Keep reading — free
The rest of the explanation, plus 2 worked examples you step through move by move.
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