For the Given Functions F and G, Find the Requested $f ( x ) = \sqrt { 7 - x } ; g ( x ) = \sqrt { x - 3 }$

Multiple Choice

For the given functions f and g, find the requested function and state its domain.
- $f ( x ) = \sqrt { 7 - x } ; g ( x ) = \sqrt { x - 3 }$
Find $f \cdot g$ .

A) $( f \cdot g ) ( x ) = \sqrt { ( 7 - x ) ( x - 3 ) } ; \{ x \mid x \geq 0 \}$
B) $( f \cdot g ) ( x ) = \sqrt { ( 7 - x ) ( x - 3 ) } ; \{ x \mid x \neq 3 , x \neq 7 \}$
C) $( f \cdot g ) ( x ) = \sqrt { - x ^ { 2 } - 21 } ; \{ x \mid x \neq 21 \}$
D) $( f \cdot g ) ( x ) = \sqrt { ( 7 - x ) ( x - 3 ) } ; \{ x \mid 3 \leq x \leq 7 \}$