Let \[f(x)={{(x+1)}^{2}}-1,\ \ (x\ge -1)\]. Then the set \[S=\{x:f(x)={{f}^{-1}}(x)\}\] is [IIT 1995]

• A. Empty
• B. {0, -1}
• C. {0, 1, -1}
• D. \[\left\{ 0,\ -1,\ \frac{-3+i\sqrt{3}}{2},\ \frac{-3-i\sqrt{3}}{2} \right\}\]