Determine Whether the Function Has an Inverse Function $f ( x ) = \left\{ \begin{array} { l } 8 x + 13 , x < - 2 \\( x + 2 ) ^ { 2 } - 3 , x \geq - 2\end{array} \right.$

Determine whether the function has an inverse function.If it does,find the inverse function. $f ( x ) = \left\{ \begin{array} { l } 8 x + 13 , x < - 2 \\( x + 2 ) ^ { 2 } - 3 , x \geq - 2\end{array} \right.$

A) $f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } \frac { x - 13 } { 8 } , x < - 2 \\\\\sqrt { x + 3 } - 2 , x \geq - 2\end{array} \right.$
B) ? $$f ^ { - 1 } ( x ) = \left\{ \begin{array} { c } \frac { x - 13 } { 8 } , x < - 2 \\\\\sqrt { x + 1 } , x \geq - 2\end{array} \right.$$
C) $$f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } \frac { x - 13 } { 8 } , x < - 3 \\\\\sqrt { x + 3 } - 2 , x \geq - 3\end{array} \right.$$
D) $f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } \frac { x + 13 } { 8 } , x < - 3 \\\\\sqrt { x + 3 } - 2 , x \geq - 3\end{array} \right.$
E) No inverse function exists.