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How many functions satisfy for every $ x $?

Source: Brazilian Math Olympiad - University Level - Galois-Noether 2018 #9

November 24, 2019
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Problem Statement

How many functions f:{1,2,3}ā†’{1,2,3}f: \left\{1,2,3\right\} \to \left\{1,2,3 \right\} satisfy f(f(x))=f(f(f(x)))f(f(x))=f(f(f(x))) for every x x ?
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