Run the Machine Backward

You'll learnto build a function’s inverse by running its machine backward, and to say when that is impossible.

An inverse function undoes what the original did: whatever journey a value is taken on, the inverse walks it home. Watch the pairs turn around, watch the graph fold across the line y = x, meet the imposter that the little minus one keeps suggesting, and see why some machines cannot be run backward at all until one lane is closed. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · f⁻¹(f(x)) = x · v4

every pair, turned around · and the machines that refuse

Before you start

What you're looking at

A machine and its reverse, the same pairs written both ways round, and a graph folded across the line y = x.

The question

What does it take to run a function backward, and when is that not possible?

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