JEE Math Practice Question

Let $$f(x) = {\sin ^{ - 1}}x$$ and $$g(x) = {{{x^2} - x - 2} \over {2{x^2} - x - 6}}$$. If $$g(2) = \mathop {\lim }\limits_{x \to 2} g(x)$$, then the domain of the function fog is :

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