Why is the answer so.....??! Kindly explain:

Question No :19

The function f : R $\to \left[1\frac{1}{2},\frac{1}{2}\right] defined as f\left(x\right)=\frac{x}{1+x^2}, is:$

A. Invertible
B. Injective but not surjective.
C.  Surjective but not injective.
D.  Neither injective nor surjective.