JEE Math Practice Question

The domain of the function $$f(x) = {\sin ^{ - 1}}\left( {{{3{x^2} + x - 1} \over {{{(x - 1)}^2}}}} \right) + {\cos ^{ - 1}}\left( {{{x - 1} \over {x + 1}}} \right)$$ is :

1. A.$$\left[ {0,{1 \over 4}} \right]$$
2. B.$$[ - 2,0] \cup \left[ {{1 \over 4},{1 \over 2}} \right]$$
3. C.$$\left[ {{1 \over 4},{1 \over 2}} \right] \cup \{ 0\} $$
4. D.$$\left[ {0,{1 \over 2}} \right]$$