A function `f` from the set of natural numbers to the set of integers defined by `f(n)={(n-1)/2,\ w h e n\ n\ i s\ od d-n/2,\ w h e n\ n\ i s\ e v e n` (a) neither one-one nor onto (b) one-one but not onto (c) onto but not one-one (d) one-one and onto both

Options

A. neither one-one nor onto
B. one-one but not onto
C. one but not one-one
D. one-one and onto both

Answer

D

Explanation

Clearly, range (f)=Z (Set of integers)
So,f is onto
We observe that distinct odd natural numbers are mapped to distinct non-negative integers and distinct even natural numbers are mapped to distinct negative integers.
So, f is one-one
Hence, f is both one-one and onto.