Determine Whether the Function Has an Inverse Function, If It $f ( x ) = 36 + x ^ { 2 } , x \leq 0$

Multiple Choice

Determine whether the function has an inverse function, If it does, find its inverse function. $f ( x ) = 36 + x ^ { 2 } , x \leq 0$

A) Yes, $f$ has an inverse function, $f ^ { - 1 } ( x ) = - \sqrt { x - 36 } , x \geq 36$
B) No, $f$ does not have an inverse function.
C) Yes, $f$ has an inverse function, $f ^ { - 1 } ( x ) = - \sqrt { x + 36 } , x \geq 36$
D) Yes, $f$ has an inverse function, $f ^ { - 1 } ( x ) = \sqrt { x - 36 } , x \geq 36$
E) Yes, $f$ has an inverse function, $f ^ { - 1 } ( x ) = - \sqrt { x - 36 } , x \leq 36$