Let \(f: \mathbb{R} \rightarrow \mathbb{R}\) be defined by \(f(x)=x^{2}-\frac{x^{2}}{1+x^{2}}\) for all \(x \in \mathbb{R}\). Then
(A) \(f\) is one-one but not onto mapping
(B) \(f\) is onto but not one - one mapping
(C) \(f\) is both one - one and onto
(D) \(f\) is neither one - one nor onto
