Yes, turns out there was a typo in the problem as it was given which explains the difficulty in solving it.
A is indeed a subset of Y which makes the statement f(f^-1(A)) true if the mapping is surjective but in the example
X={1,3,5} Y={2,4,6,8} f:X->Y = {(1,2),(3,4),(5,6)}
Where f is...