JEE Math Practice Question

Let $$f\left( x \right) = \left\{ {\begin{matrix} { - 1} & { - 2 \le x < 0} \\ {{x^2} - 1,} & {0 \le x \le 2} \\ \end{matrix} } \right.$$ and $$g(x) = \left| {f\left( x \right)} \right| + f\left( {\left| x \right|} \right).$$ Then, in the interval (–2, 2), g is :

1. A.non continuous
2. B.differentiable at all points
3. C.not differentiable at two points
4. D.not differentiable at one point