Final answer:
Both functions A) f(n)=8+3(n^-1) and B) f(n)=3+8(n^-1) are non-recursive as they are independently defined for any value of 'n' and do not require iterative or recursive computation.
Step-by-step explanation:
The question pertains to which function is non-recursive out of the two options given: A) f(n)=8+3(n^-1) or B) f(n)=3+8(n^-1). A non-recursive function is one that can be computed in a straightforward manner without the need for repeated substitution of previous values of the function.
Both functions A and B are actually non-recursive since they do not refer back to previous values of the function. Rather, they are algebraically defined for any value of 'n' independently of other values. Option A has the term 3(n^-1) which using rules of exponents can be rewritten as 3/n, and option B can similarly be rewritten with 8(n^-1) as 8/n. Neither function requires previous values to determine the result for any given 'n'.
It's also worth noting that negative exponents flip the construction to the denominator (as per A.9), indicating division, which does not make a function recursive. Furthermore, these function forms do not align with series expansions or the binomial theorem.