Reversible data transformations?

Question

Mathematics

Question [2] "Origins"
By what criteria can one judge that the data obtained after the transformation can be reversely transformed if after the transformation they have a radically different nature and structure?

Answer 1

If each transformation in the chain is reversible, then the result will be reversible, as a proof, consider the following algorithm:
X <- initial data
F1 <- reversible transformation, denote its inverse F1'
F2 <- reversible transformation, denote its inverse F2'
. .. FN <- reversible transformation, denote its inverse
by FN'
Then, after applying all the transformations, we get some data X':
X' = FN(...(F2(F1(X))))
transformations:
X = F1'(F2'(...(FN'(X'))))