Find the analytic formula of the following functions: (1) if f (2x + 1) = 4x2 + 2x + 1, find the analytic formula of F (x); (2) if 2F (x) - f (- x) = x + 1, find the analytic formula of F (x)

Find the analytic formula of the following functions: (1) if f (2x + 1) = 4x2 + 2x + 1, find the analytic formula of F (x); (2) if 2F (x) - f (- x) = x + 1, find the analytic formula of F (x)

(1) Let 2x + 1 = t, then x = T-12; f (T) = 4 (T-12) 2 + 2 · T-12 + 1 = t2-t + 1; f (x) = x2-x + 1. (2) from 2F (x) - f (- x) = x + 12F (- x) - f (x) = - x + 1, the solution is f (x) = X3 + 1