Show That $f$ And $g$ Are Functions by Using the Definition of Inverse Functions

Show that $f$ and $g$ are functions by using the definition of inverse functions. $f ( x ) = \frac { 1 } { x } , g ( x ) = \frac { 1 } { x }$

A) $f ( g ( x ) ) = x , g ( f ( x ) ) = x - 1$
B) $f ( g ( x ) ) = x - 1 , g ( f ( x ) ) = x$
C) $f ( g ( x ) ) = x , g ( f ( x ) ) = x$
D) $f ( g ( x ) ) = x , g ( f ( x ) ) = x ^ { - 1 }$
E) $f ( g ( x ) ) = x ^ { - 1 } , g ( f ( x ) ) = x$