JEE Math Practice Question

Let ƒ : (1, 3) $$ \to $$ R be a function defined by $$f(x) = {{x\left[ x \right]} \over {1 + {x^2}}}$$ , where [x] denotes the greatest integer $$ \le $$ x. Then the range of ƒ is

1. A.$$\left( {{2 \over 5},{1 \over 2}} \right) \cup \left( {{3 \over 4},{4 \over 5}} \right]$$
2. B.$$\left( {{3 \over 5},{4 \over 5}} \right)$$
3. C.$$\left( {{2 \over 5},{4 \over 5}} \right]$$
4. D.$$\left( {{2 \over 5},{3 \over 5}} \right] \cup \left( {{3 \over 4},{4 \over 5}} \right)$$