Let R be a commutative ring with identity and c,d R with c a unit. (a)

Let R be a commutative ring with identity and c,d ϵ R with c a unit.

(a) Show that the assignment x|→ cx + b induces a unique automorphism of R[x] that is the identity of R. What is its inverse?

(b) If D is an integral domain, then show that every automorphism of D[x] that is the identity on D is of the type described in (a).