For the given functions f and g , find the indicated composition.
-$$\begin{array} { l }
f ( x ) = \frac { 8 } { x + 4 } , \quad g ( x ) = \frac { 6 } { 5 x } \
( f \circ g ) ( x )
\end{array}$$
A) $\frac { 40 x } { 6 - 20 x }$

B) $\frac { 6 x + 24 } { 40 x }$

C) $\frac { 8 x } { 6 + 20 x }$

D) $\frac { 40 x } { 6 + 20 x }$

Question

For the given functions f and g , find the indicated composition.
-$$\begin{array} { l } 
f ( x ) = \frac { 8 } { x + 4 } , \quad g ( x ) = \frac { 6 } { 5 x } \
( f \circ g ) ( x )
\end{array}$$
A) $\frac { 40 x } { 6 - 20 x }$

B) $\frac { 6 x + 24 } { 40 x }$

C) $\frac { 8 x } { 6 + 20 x }$

D) $\frac { 40 x } { 6 + 20 x }$

Quizplus · Accepted Answer

To find $(f \circ g)(x)$, we substitute $g(x)$ into $f(x)$, resulting in $f(g(x)) = f\left(\frac{6}{5x}\right) = \frac{8}{\frac{6}{5x} + 4}$. Simplifying this expression, we get $\frac{8}{\frac{6}{5x} + \frac{20x}{5x}} = \frac{8}{\frac{6+20x}{5x}} = \frac{8 \cdot 5x}{6+20x} = \frac{40x}{6+20x}$, which matches option D.

For the Given Functions F and G , Find the Indicated