NDA Math Functions

$f: X \rightarrow Y$ 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 $a \in Z$ Hence, the function is not one one For a function $f: X \rightarrow Y$, 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.