I need some clue with the inverse image...
Show that the subset X of polynominals in R_{2n}[X] all of whose odd coefficients a_{2i+1} are zero forms a subspace of R_{2n}[X]. Describe D^{-->}(X) and D^{<--}(X).
Do D^{-->}(X) mean the set of polynomials whose even coefficients are zero, and D^{<--}(X) mean the set of polynomials whose odd coefficients are zero?
Thank you in advance for any help you can provide...