Please answer b, d, and e

6. Determine whether each of these proposed definitions is a valid recursive definition of a function f from the set of nonnegative integers to the set of integers. If f is well defined, find a formula for f(n) when nis a nonnegative integer and prove that your formula is valid. b) f(0)= 1, f(l) = 0, f(2)= 2, f(n)=2f(n-3) for n 3 c) f (0) 0, f(l)-1, f(n) 2f(n+ 1) for n 2 d) f(0) = 0,f( 1 ) = 1,f(n) = 2f(n-1) for n 21 e) f(0) 2, f (n) f (n 1ifn is odd and n 2 1 and f(n) = 2f(n-2) if n >2