Thread: polynomials direct and 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...

I need some clue with the inverse image...