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Determine if each of the following recursive definition is a valid recursive definition of a function...

  1. Determine if each of the following recursive definition is a valid recursive definition of a function f from a set of non-negative integers. If f is well defined, find a formula for f(n) where n is non-negative and prove that your formula is valid.
    1. f(0) = 1, f(n) = -f(n-1) + 1 for n ≥ 1
    2. f(0) = 0, f(1) = 1, f(n) = 2f(n-1) +1 for n ≥ 1
    3. f(0) =0, f(n) = 2f(n-1) + 2 for n ≥ 1
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Proof is done using induction.

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