JEE Math Practice Question

If the function $$f(x) = \left\{ {\begin{matrix} {{1 \over x}{{\log }_e}\left( {{{1 + {x \over a}} \over {1 - {x \over b}}}} \right)} & , & {x < 0} \\ k & , & {x = 0} \\ {{{{{\cos }^2}x - {{\sin }^2}x - 1} \over {\sqrt {{x^2} + 1} - 1}}} & , & {x > 0} \\ \end{matrix} } \right.$$ is continuous at x = 0, then $${1 \over a} + {1 \over b} + {4 \over k}$$ is equal to :

1. A.$$-$$5
2. B.5
3. C.$$-$$4
4. D.4