For the Given Functions F and G, Find the Requested $$f ( x ) = \sqrt { 6 - x } ; g ( x ) = \sqrt { x - 2 }$$

Multiple Choice

For the given functions f and g, find the requested function and state its domain.
- $$f ( x ) = \sqrt { 6 - x } ; g ( x ) = \sqrt { x - 2 }$$
Find $f \cdot g$ .

A) $( f \cdot g ) ( x ) = \sqrt { ( 6 - x ) ( x - 2 ) } ; \{ x \mid x \neq 2 , x \neq 6 \}$
B) $( \mathrm { f } \cdot \mathrm { g } ) ( \mathrm { x } ) = \sqrt { ( 6 - \mathrm { x } ) ( \mathrm { x } - 2 ) } ; \{ \mathrm { x } \mid 2 \leq \mathrm { x } \leq 6 \}$
C) $( f \cdot g ) ( x ) = \sqrt { ( 6 - x ) ( x - 2 ) } ; \{ x \mid x \geq 0 \}$
D) $( \mathrm { f } \cdot \mathrm { g } ) ( \mathrm { x } ) = \sqrt { - \mathrm { x } ^ { 2 } - 12 } ; \{ \mathrm { x } \mid \mathrm { x } \neq 12 \}$