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Technically it would be a cat spitting a fish out.
Yeah, a better analogy would be x(f)
No, it would be some unspecified object that turns cat poop into fish. The function is 🐟 → 💩, so the inverse is 💩→ 🐟.
Discrete mathematics in a nutshell
This is saying that if a cat eats a fish, and then another cat crawls into a fake giant fish's mouth, the universe returns to the state it was in before the first cat ate the fish.