89 let r[x] denote the vector space of all real polynomials. let d: r[x] rx]. denote the map df = vf. then, 1. dis one-one. 2. dis onto. 3. there exists e: r[x]

89 Let R[x] denote the vector space of all real polynomials. Let D: R[x] Rx]. denote the map Df = Vf. Then, 1. Dis one-one. 2. Dis onto. 3. There exists E: R[x]> R[2] so that D(EF)) f,Vf. 4. There exists E: R[x] > R[x] so that E(D) =f,Vf.