Which of the following maps C[X] → C[X] are ring homomorphisms? Select all that apply: O The map f(X) H f(X+2). O The map f(X) f(2X+1). O The map f(X)→ f(X)+2. O The map f(X) H 2f(X) – 1.

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A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

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A: Given that R is a ring. deg{f(x)}=3 deg{g(x)}=4

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Q: Construct a nontrivial homomorphism $: Zg → Zı5 >

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Q: The function f : Z → Z2 given by f(x) = [x] has these properties: • Væ, y E Z, f(x + y) = f(x)+ f(y)…

A: Ans - ring homomorphism

Q: We denote the set of polynomials with real coefficients as R[X]:= {ao + a₁X + a₂X² +.... + a₂X": n€…

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A: Since you have asked multiple questions, we will solve the Question (k) and (l) for you. If you want…