Computation Theory - Show that the family of regular languages is closed under tail(L) = {y : xy ∈ L for some x ∈ Σ ∗ }

Question

The tail of a language is the set of all suffixes of its strings, that is tail(L) = {y : xy ∈ L for some x ∈ Σ ∗ }.

How do I show that the family of regular languages is closed under this operation.

Answer 1

Suffix(L)=Reverse(prefix(Reveres(L))) //we know reverse and prefix closed under regular Hence suffix(L) also regular

i.e. L={abc} then suffix(L)={^,c,bc,abc}