**Problem 8:** Determine if each of the following recursive definitions 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.a. \( f(0) = 2, \, f(1) = 3, \, f(n) = f(n-1) - 1 \) for \( n \geq 2 \)b. \( f(0) = 1, \, f(1) = 2, \, f(n) = 2f(n-2) \) for \( n \geq 2 \)

Recursive Function: In mathematics and computer science, a recursive function is one that defines…

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