Let $f(x) =(x+1)^2-1 , ( x \leq -1)$. Then the set $S= \{x : f(x) =f^{-1}(x)\}$ is

Question

$\begin{array}{1 1} \{0,-1,\large\frac{-3 +i \sqrt 3}{2},\frac{-3 -i \sqrt 3}{2} \\ {0,1,-1} \\ {0,-1} \\ empty \end{array}$