Determine Whether the Function Has an Inverse Function $f ( x ) = \left\{ \begin{array} { l } x + 2 , x < 0 \\2 - x , x \geq 0\end{array} \right.$

Multiple Choice

Determine whether the function has an inverse function.If it does, find the inverse function.
$f ( x ) = \left\{ \begin{array} { l } x + 2 , x < 0 \\2 - x , x \geq 0\end{array} \right.$

A) $f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } 2 + x , x \geq 0 \\x - 2 , x < 0\end{array} \right.$
B) $f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } 2 + x , x \geq 0 \\x - 2 , x < 0\end{array} \right.$ .
C) $f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } x - 2 , x \geq 0 \\2 + x , x < 0\end{array} \right.$
D) $f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } x + 2 , x \geq 0 \\2 - x , x < 0\end{array} \right.$
E) No inverse