For the given functions f and g , find the indicated composition.
-$$f ( x ) = \frac { 1 } { x - 7 } , \quad g ( x ) = \frac { 5 } { 6 x }$$
$( f g ) ( x )$
A) $\frac { 5 x - 35 } { 6 x }$
B) $\frac { 1 x } { 5 - 42 x }$
C) $\frac { 6 x } { 5 + 42 x }$
D) $\frac { 6 x } { 5 - 42 x }$

Question

Quizplus · Accepted Answer

To find $(fg)(x)$, we substitute $g(x)$ into $f(x)$: $f(g(x)) = \frac{1}{\frac{5}{6x} - 7} = \frac{1}{\frac{5-42x}{6x}} = \frac{6x}{5-42x}$.

For the Given Functions F and G , Find the Indicated