I am finding it hard to solve the following problem.
Let $A$ is a set and $f : A \rightarrow A$ and $g : A \rightarrow A$. If $f = g \circ f$, must $g$ be an identity function always?
Will there be any counterexamples to show that $g$ must not be a identity function?
Must $g$ be the identity if $f = g \circ f$?
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functions
elementary-set-theory
examples-counterexamples
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2$g |_{f(A)}$ is an identity. – 2012-05-10