Answer to Question #38610 in Math for Sujata Roy

Question

Consider two languages L1 and L2 each on the alphabet sigma. Let
f: sigma->sigma be a polynomial time computable bijection such that
( for all x [ x belongs to L1 iff f(x) belongs to L2]. Further, let f1 be also polynomial time
commutable.
Which of the following CANNOT be true?
(A) L1 belongs to P and L2 finite
(B) L1 belongs to NP and L2 belongs to P
(C) L1 is undecidable and L2 is decidable
(D) L1 is recursively enumerable and L2 is recursive