Let V = P, (R), equipped with the inner product defined by (f, 9) = | f(t)g(t) dt. Then {1.2/3(- с — x + is an orthonormal basis for V. (You do not need to verify this.) Let T:V → R be the linear...

Extracted text: Let V = P, (R), equipped with the inner product defined by (f, 9) = | f(t)g(t) dt. Then {1.2/3(- с — x + is an orthonormal basis for V. (You do not need to verify this.) Let T:V → R be the linear functional on V defined by T(f) = f'(1/2) (i.e. T(f(x)) is the derivative of f(x), evaluated at x = 1/2). Find a polynomial h e V such that T(f) (f, h) for all f e V. Enter the coefficients of h(x) below. = h(x) = x2 + x + If any coefficient is not an integer, enter its decimal representation up to three digits after the decimal point.