"Use the principles of mathematical induction to show that the value at each positive integer of a function defined recursively is uniquely determined"
I have a problem understanding what exactly it wants me to show. Does it want me to show that
A: for a positive integer $n_1$, the value of the recursive function $f(n_1)$ is unique, meaning that there are no other positive integers $n$ such that $f(n)=f(n_1)$ (show that $f$ is injective)
B: functions $f$ and $g$ must be the same function if for every positive integer $n$: $f(n)=g(n)$, therefore proving uniqueness.
I have solved it for B but not sure about my solution in A. Do I continue with A or have I solved it assuming my solution is correct in B?