Write the function F(x) as a composition of f, g, or h.
-$\begin{array} { l }
f ( x ) = x ^ { 2 } - 2 \quad g ( x ) = - 6 x \quad h ( x ) = \sqrt { x + 7 } \
F ( x ) = \sqrt { - 6 x + 7 }
\end{array}$
A) $F ( x ) = ( f \circ h ) ( x )$
B) $F ( x ) = ( g \circ h ) ( x )$
C) $F ( x ) = ( h \circ f ) ( x )$
D) $F ( x ) = ( h \circ g ) ( x )$

Question

Write the function F(x) as a composition of f, g, or h.
-$\begin{array} { l } 
f ( x ) = x ^ { 2 } - 2 \quad g ( x ) = - 6 x \quad h ( x ) = \sqrt { x + 7 } \
F ( x ) = \sqrt { - 6 x + 7 }
\end{array}$
A) $F ( x ) = ( f \circ h ) ( x )$
B) $F ( x ) = ( g \circ h ) ( x )$
C) $F ( x ) = ( h \circ f ) ( x )$
D) $F ( x ) = ( h \circ g ) ( x )$

Quizplus · Accepted Answer

F(x) can be expressed as $h(g(x))$, where $g(x) = -6x$ is applied first, followed by $h(x) = \sqrt{x + 7}$, resulting in $F(x) = \sqrt{-6x + 7}$.

Write the Function F(x) as a Composition of F, G f(x)=x2−2g(x)=−6xh(x)=x+7F(x)=−6x+7\begin{array} { l } f ( x ) = x ^ { 2 } - 2 \quad g ( x ) = - 6 x \quad h ( x ) = \sqrt { x + 7 } \\F ( x ) = \sqrt { - 6 x + 7 }\end{array}f(x)=x2−2g(x)=−6xh(x)=x+7​F(x)=−6x+7​​

Write the Function F(x) as a Composition of F, G $\begin{array} { l } f ( x ) = x ^ { 2 } - 2 \quad g ( x ) = - 6 x \quad h ( x ) = \sqrt { x + 7 } \\F ( x ) = \sqrt { - 6 x + 7 }\end{array}$