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  3. 7. let n ∈ n with n > 1 and let p be the s

7. Let n ∈ N with n > 1 and let P be the set...

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Advance Math

7. Let n ∈ N with n > 1 and let P be the set of polynomialswith coefficients in R.

(a) We define a relation, T, on P as follows: Let f, g ∈ P. Thenwe say f T g if f −g = c for some c ∈ R. Show that T is anequivalence relation on P.

(b) Let R be the set of equivalence classes of P and let F : R →P be the derivative operator defined as F([f]) = df/dx. Is F welldefined (i.e. is it a function)? Is it surjective? Is itinjective?

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