when n=2,4,6, 8.1.... f(n)={1,2,3.....} when n=1,3,5... f(n)={0,−1,−2,−3...} ∴ Function is one-one and onto
Clealy f is one-one function as for each even natural number we have different image as positive integer and for odd natural number image set is set of non-positive integer. also their are no any integer for which pre image does not exists. Henceone-one onto