For the given functions f and g, find the requested function and state its domain.
-$f ( x ) = \sqrt { x + 13 } ; g ( x ) = \frac { 4 } { x }$ Find f · g.
A) $( f \cdot g ) ( x ) = \frac { \sqrt { 4 x + 52 } } { x } ; \{ x \mid x \geq - 13 , x \neq 0 \}$
B) $( f \cdot g ) ( x ) = \sqrt { \frac { 17 } { x } } ; \{ x \mid x \neq 0 \}$
C) $( f \cdot g ) ( x ) = \frac { 4 \sqrt { x + 13 } } { x } ; \{ x \mid x \geq - 13 , x \neq 0 \}$
D) $( f \cdot g ) ( x ) = \sqrt { \frac { 4 x + 52 } { x } } ; \{ x \mid x \geq - 13 , x \neq 0 \}$

Question

For the given functions f and g, find the requested function and state its domain.
-$f ( x ) = \sqrt { x + 13 } ; g ( x ) = \frac { 4 } { x }$ Find f · g. 
A) $( f \cdot g ) ( x ) = \frac { \sqrt { 4 x + 52 } } { x } ; \{ x \mid x \geq - 13 , x \neq 0 \}$
B) $( f \cdot g ) ( x ) = \sqrt { \frac { 17 } { x } } ; \{ x \mid x \neq 0 \}$
C) $( f \cdot g ) ( x ) = \frac { 4 \sqrt { x + 13 } } { x } ; \{ x \mid x \geq - 13 , x \neq 0 \}$
D) $( f \cdot g ) ( x ) = \sqrt { \frac { 4 x + 52 } { x } } ; \{ x \mid x \geq - 13 , x \neq 0 \}$

Quizplus · Accepted Answer

The product $f \cdot g$ is found by multiplying $f(x) = \sqrt{x + 13}$ and $g(x) = \frac{4}{x}$ together, resulting in $\frac{4\sqrt{x + 13}}{x}$. The domain is $x \geq -13$ to ensure the radicand is non-negative and $x \neq 0$ to avoid division by zero.

For the Given Functions F and G, Find the Requested f(x)=x+13;g(x)=4xf ( x ) = \sqrt { x + 13 } ; g ( x ) = \frac { 4 } { x }f(x)=x+13​;g(x)=x4​

For the Given Functions F and G, Find the Requested $f ( x ) = \sqrt { x + 13 } ; g ( x ) = \frac { 4 } { x }$