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 n is a nonnegative integer and prove that your formula is valid. a. f (0) = 0. f (n) = 2 f (n − 2) for n ≥ 1
b. f (0) = 1, f( 1) = f (n − 1) − 1 for n ≥1
c. f (0) = 2, f (1) = 3, f (n) = f(n − 1) − 1 for n ≥ 2
d. f (0)= 1. f (1) = 2, f (n) = 2 f (n − 2) for n ≥2
e. f (0) = 1, f(n) = 3 f (n −1) if n is odd and n ≥1 and f(n) = 9 f(n − 2) if n is even and n ≥2