Calculate $g ( x )$ , Where $g = f ^ { - 1 }$

Multiple Choice

Calculate $g ( x )$ , where $g = f ^ { - 1 }$ . State the domain and range of $g$ . Calculate $g ^ { \prime } ( a )$
$$f ( x ) = \frac { 1 } { x - 3 } , x > 3 ; a = 2$$

A) $g ( x ) = 3 + \frac { 1 } { x } , g ^ { \prime } ( 2 ) = - \frac { 1 } { 4 }$ , domain $= ( 0 , \infty )$ , range $= ( 3 , \infty )$
B) $g ( x ) = 4 + \frac { 1 } { x } , g ^ { \prime } ( 2 ) = - \frac { 1 } { 4 }$ , domain $= ( 0 , \infty )$ , range $= ( 4 , \infty )$
C) $g ( x ) = 2 + \frac { 1 } { x } , g ^ { \prime } ( 2 ) = - \frac { 1 } { 2 }$ , domain $= ( 0 , \infty )$ , range $= ( 3 , \infty )$
D) $g ( x ) = 4 + \frac { 1 } { 2 x } , g ^ { \prime } ( 2 ) = - \frac { 1 } { 8 }$ , domain $= ( 0 , \infty )$ , range $= ( 3 , \infty )$
E) $g ( x ) = 1 + \frac { 3 } { x } , g ^ { \prime } ( 2 ) = - \frac { 3 } { 4 }$ , domain $= ( 0 , \infty )$ , range $= ( 1 , \infty )$