The Function $f ( x ) = \sqrt { x ^ { 2 } - 5 }$

Multiple Choice

The function $f ( x ) = \sqrt { x ^ { 2 } - 5 }$ is one-to-one on the domain $x \leq - \sqrt { 5 }$ . Find $f ^ { - 1 } ( x )$ .

A) $\quad f ^ { - 1 } ( x ) = x ^ { 2 } + 5$
B) $f ^ { - 1 } ( x ) = \sqrt { x ^ { 2 } + 5 }$
C) $f ^ { - 1 } ( x ) = \frac { 1 } { \sqrt { x ^ { 2 } - 5 } }$
D) $\quad f ^ { - 1 } ( x ) = - \sqrt { x ^ { 2 } + 5 }$
E) $f ^ { - 1 } ( x ) = - \sqrt { x ^ { 2 } - 5 }$