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

Question

Quizplus · Accepted Answer

The composition $(g \circ f)(x)$ means applying $f$ first and then $g$. So, first, we calculate $f(x) = \sqrt{x + 5}$, and then we substitute this into $g(x)$ to get $g(f(x)) = -\frac{7}{\sqrt{x + 5}}$, which matches option D.

For the Given Functions F and G , Find the Indicated