For the given functions f and g , find the indicated composition.
-$$f ( x ) = \sqrt { x + 4 } , \quad g ( x ) = - \frac { 5 } { x }$$
$( g f ) ( x )$
A) $- \frac { 1 } { \sqrt { 5 x + 4 } }$
B) $\sqrt { - \frac { 5 } { x } + 4 }$
C) $\frac { 5 } { \sqrt { - x + 4 } }$
D) $- \frac { 5 } { \sqrt { x + 4 } }$

Question

Quizplus · Accepted Answer

The composition $(g \circ f)(x) = g(f(x))$ means we substitute $f(x)$ into $g(x)$. So, $g(f(x)) = g(\sqrt{x + 4}) = -\frac{5}{\sqrt{x + 4}}$, which matches option D.

For the Given Functions F and G , Find the Indicated