For the given functions f and g , find the indicated composition.
-$$f ( x ) = \frac { 3 } { x + 6 } , \quad g ( x ) = \frac { 5 } { 6 x }$$
$( f \circ g ) ( x )$
A) $\frac { 18 x } { 5 - 36 x }$
B) $\frac { 3 x } { 5 + 36 x }$
C) $\frac { 18 x } { 5 + 36 x }$
D) $\frac { 5 x + 30 } { 18 x }$

Question

Quizplus · Accepted Answer

To find $(f \circ g)(x)$, we substitute $g(x)$ into $f(x)$: $f(g(x)) = f\left(\frac{5}{6x}\right) = \frac{3}{\frac{5}{6x} + 6} = \frac{3}{\frac{5}{6x} + \frac{36x}{6x}} = \frac{3}{\frac{5 + 36x}{6x}} = \frac{3 \cdot 6x}{5 + 36x} = \frac{18x}{5 + 36x}$.

For the Given Functions F and G , Find the Indicated