2. (a) Suppose a function f(n) is defined by the following recursive formula. f(n) = Use the guess-and-check method to get a closed-form formula for f(n). That is, guess a formula for f(n) and use induction to prove that your guess is correct. Guess: The following table suggests that a fo rmula for f(n) may be f(n) f(n) Check: We can prove that this formula holds by strong /weak (regular) induction on n Provide the proof of induction (b) Suppose a function g(n) is defined by the following recursive formula. g(n) = 2n * g(n-1), g(1) = 2. Use the unraveling method to get a closed-form formula for g(n). Make sure to show your work