If $f(f(x)) = f(x) \quad \forall \space x$ then $f$ is idempotent.
If $g(f(x)) = f(x) \quad \forall \space x$ then is there a term to describe the relationship between $g$ and $f$?
2026-03-27 16:26:55.1774628815
Is there a name for a relationship like idempotence between two functions?
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I don't think there is a name for it, but the property could be stated as "$g$ is the identity on the range of $f$".