Determine whether each of these proposed definitions is a valid recursive definition of a function f...

 

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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) = 1, f(n) = -f(n-1) for n ≥ 1 b) f(0) = 1, f(1) = 0, f (2) = 2, f(n) = 2f (n-3) for n ≥ 3 c) f(0) = 0, f(1) = 1, f(n) = 2f (n+1) for n 22 d) f(0) = 0, f(1) = 1, f (n) = 2f (n-1) for n ≥ 1 e) f (0) = 2, f(n) = f(n-1) if n is odd and n 21 and f(n) = 2f (n-2) if n ≥2 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) = 1, f(n) = -f(n-1) for n ≥ 1 b) f(0) = 1, f(1) = 0, f (2) = 2, f(n) = 2f (n-3) for n ≥ 3 c) f(0) = 0, f(1) = 1, f(n) = 2f (n+1) for n 22 d) f(0) = 0, f(1) = 1, f (n) = 2f (n-1) for n ≥ 1 e) f (0) = 2, f(n) = f(n-1) if n is odd and n 21 and f(n) = 2f (n-2) if n ≥2

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a This formula is well defined as given fn1 we can find fn using fn f... View the full answer