Question

Let f be a function with the following properties:
(i) f(1) = 1
(ii) f(2n) = n.f(n) for any positive integer n.
What is the value of f(2¹⁰⁰) ?
(A) 2⁵⁰⁵⁰
(B) 2⁹⁹
(C) 2¹⁰⁰
(D) 2⁴⁹⁵⁰
Answer with proper explanation.

Answer 1

Refer to  the attachment.