tie f ( x ) = an X" + an- 1 . .. n 8 fl( x ) = ragn - 1 of ( n - 1 ) an-, Jn- + .... S a. G Pu ( R) f *( x ) G Pu ( R ) ( Vos xen ) Pu( ) is a rected space over field R. g l x ) = C . f ( x ) + C , f ( x ) + (z f" ( X)+ .... + Cuf ( x ) is a linear combination of elements of Pu (R ) Hence (x) 6 PM (R ) ok, but can EVERY g be expressed in this way?24. Let f(x) be a polynomial of degree n in Pn(R). Prove that for any g(x) E Pn (R) there exist scalars co, C1, . .., On such that g(x) = cof (x) + cIf'(x) + c2f"(x) + ... + enf(?)(x), where f(n) (x) denotes the nth derivative of f(x)