UPSC NDA I 2014 Mathematics Paper

f:X→Y
For a function to be one one or injective, every element in the domain is the image of at most one element of it's co-domain.
In simple words, no value of y must be same for 2 or more different values of x. For f(x)=|x|, we see that f(a)=f(−a), for a∈Z
Hence, the function is not one one
For a function f:X→Y, to be surjective, every element y in the co-domain Y must be linked with at least one element x in the domain.
Every element in the co-domain of f(x)=|x| is linked to at-least one element in domain.
Thus, f(x)=|x| is onto but not one one.