Run the Machine Backward

You'll learnto build a function's inverse by running its machine backward.

An inverse function undoes what the original did: whatever journey f takes an input on, f⁻¹ walks it home. Watch the pairs swap, watch the graph fold across y = x, meet the imposter that the −1 exponent keeps suggesting — and see why some machines cannot be run backward at all until you close a lane.

8 STEPS · 6 QUICK CHECKS · f⁻¹(f(x)) = x · v3

f⁻¹

Before you start

What you're looking at

An input-output table whose arrows are about to be reversed, and a graph ready to fold across y = x.

The question

If f takes this input to that output, what does the inverse do?

Watch for

Inverse means undo, not reciprocal — the −1 is not an exponent — and why some machines need a lane closed first.

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