Given F(x) and G(x), Find the Indicated Composition and State $\mathrm { f } ( \mathrm { x } ) = \frac { 1 } { \mathrm { x } - 5 }$

Multiple Choice

Given f(x) and g(x) , find the indicated composition and state its domain.
-For $\mathrm { f } ( \mathrm { x } ) = \frac { 1 } { \mathrm { x } - 5 }$ and $g ( x ) = \frac { 7 } { \mathrm { x } }$ , what is the domain of $g \cdot \mathrm { f }$ ?

A) $( - \infty , 0 ) \cup \left( 0 , \frac { 7 } { 5 } \right) \cup \left( \frac { 7 } { 5 } , \infty \right)$
B) $( - \infty , 0 ) \cup ( 0 , \infty )$
C) $( - \infty , 0 ) \cup ( 0,5 ) \cup ( 5 , \infty )$
D) $( - \infty , 5 ) \cup ( 5 , \infty )$