Unsort: remembering a permutation and undoing it

Question

Suppose I have a function f that takes a vector v and returns a new vector with the elements transformed in some way. It does that by calling function g that assumes the vec

Answer 1

Here's a "sorting wrapper" pattern suggested by Michael Pilat earlier

Clear[g];
g[a_] := If[OrderedQ[a], a^2, Print["Failed"]];
g[{3, 2, 1}]
g[a_] := g[Sort@a][[Ordering@Ordering@a]] /; Not[OrderedQ[a]];
g[{3, 2, 1}]