Please explain how you get the answer, thanks

Let f(n) denote iterated exponentiation with base 2. Formally, it is defined as folloWS if n- 0 if n> 1 f(n) 2f(n-1) 2, f(3)22, f(4)222", and so For your intuition, consider f(1) - 2, f(2) - 2 on. In words, f(n) is a tower of height n of powers of 2. (b.1) Prove by induction that 2" 2 2n and argue that it implies f(m+1) 2 2f(m) (b.2) Prove by induction that f(n) > n (b.3) Let = {a}. Prove that L {af(n) : n 0} is not regular using the pumping lemma. SO Let f(n) denote iterated exponentiation with base 2. Formally, it is defined as folloWS if n- 0 if n> 1 f(n) 2f(n-1) 2, f(3)22, f(4)222", and so For your intuition, consider f(1) - 2, f(2) - 2 on. In words, f(n) is a tower of height n of powers of 2. (b.1) Prove by induction that 2" 2 2n and argue that it implies f(m+1) 2 2f(m) (b.2) Prove by induction that f(n) > n (b.3) Let = {a}. Prove that L {af(n) : n 0} is not regular using the pumping lemma. SO