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

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

(a) We define a relation, T, on P as follows: Let f, g ∈ P. Then we say f T g if f −g = c for some c ∈ R. Show that T is an equivalence 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 well defined (i.e. is it a function)? Is it surjective? Is it injective?

Expert Solution

Colby Messinger answered 2 years ago

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

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