For the following statements, consider the functions f(n), g(n) and constant c such that f(n) 0, g(n) 0, and c > 0. Indicate whether the statements are true or false. If true prove the statement by providing a formal argument based on the definition of asymptotic notation, otherwise, provide a counter-example to prove that they are false.

(di) f(2n) = f(n)). (d) If f(n) = O(n), then f (2n) = O(n). (d3) If f(n) = O(n"), then f(2n) = f(n))