Answer Happy

Question is in Picture. This is from Abstract Algebra: Modules.
Please answer if you are familiar with the topic and can answer in
a clear and detailed way. The textbook used is: Abstract Algebra -
3rd Edition by David S. Dummit, Richard M. Foote. Thank you!
3. If R is a commutative ring, show that the map 4: R[x] → R[x] defined by (p(x)) = xp(x) is an R-module homomorphism, but not a ring homomorphism. =