Undoing Operations

Pre-Calculus · Axiom Academy

Every function is a chain of moves — and every chain can be run backward. That backward run is the inverse. If you know the output, can you find the input? A function is a machine: feed it an input, it runs a chain of operations, out comes an output. But suppose you only have the output and need the original input back. You don't guess — you run the machine backward , undoing each step. That backward machine is the inverse function , and you're about to watch one in action. This machine does two things in order: ×2 then +3 . Watch the input 4 flow forward to the output 11 — then watch the sweep reverse and undo the chain: subtract 3 first , divide by 2 last , landing right back on 4. The inverse isn't a new idea — it's the same machine, run in reverse, undoing each step in the opposite order. It works for every input, not just 4 Slide to choose any input. The top row runs it forward ( ×2 then +3 ); the bottom row runs that output backward ( −3 then ÷2 ). Watch the recovered value: no matter what you pick, the undo chain hands you the original input back. Reverse the steps and their order: −3 must come before ÷2. Do them in the wrong order and you land on the wrong number — order is half of undoing. Hand it any output — it finds the input

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