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) $( f \cdot g ) ( x ) = \sqrt { ( 7 - x ) ( x - 3 ) } ; \{ x \mid 3 \leq x \leq 7 \}$

Question

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) $( f \cdot g ) ( x ) = \sqrt { ( 7 - x ) ( x - 3 ) } ; \{ x \mid 3 \leq x \leq 7 \}$

Quizplus · Accepted Answer

The product of $f(x)$ and $g(x)$ is indeed $\sqrt{(7-x)(x-3)}$. The domain of this function is determined by the conditions that $7-x \geq 0$ and $x-3 \geq 0$, which simplify to $x \leq 7$ and $x \geq 3$, respectively. Therefore, the domain is $\{x \mid 3 \leq x \leq 7\}$.

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

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