Write the function F(x) as a composition of f, g, or h.
-$$\begin{array} { l }
f ( x ) = x ^ { 2 } + 6 \quad g ( x ) = - 2 x \quad h ( x ) = \sqrt { x - 4 } \
F ( x ) = \sqrt { - 2 x - 4 }
\end{array}$$
A) $\mathrm { F } ( \mathrm { x } ) = ( \mathrm { h } \circ \mathrm { g } ) ( \mathrm { x } )$
B) $\mathrm { F } ( \mathrm { x } ) = ( \mathrm { h } \circ \mathrm { f } ) ( \mathrm { x } )$
C) $F ( x ) = ( g \circ h ) ( x )$
D) $F ( x ) = ( f \circ h ) ( x )$

Question

Write the function F(x) as a composition of f, g, or h.
-$$\begin{array} { l } 
f ( x ) = x ^ { 2 } + 6 \quad g ( x ) = - 2 x \quad h ( x ) = \sqrt { x - 4 } \
F ( x ) = \sqrt { - 2 x - 4 }
\end{array}$$
A) $\mathrm { F } ( \mathrm { x } ) = ( \mathrm { h } \circ \mathrm { g } ) ( \mathrm { x } )$
B) $\mathrm { F } ( \mathrm { x } ) = ( \mathrm { h } \circ \mathrm { f } ) ( \mathrm { x } )$
C) $F ( x ) = ( g \circ h ) ( x )$
D) $F ( x ) = ( f \circ h ) ( x )$

Quizplus · Accepted Answer

F(x) can be expressed as h(g(x)) because g(x) = -2x transforms into -2x - 4 when -4 is added, and then h takes the square root of that result, matching F(x) = sqrt(-2x - 4).

Write the Function F(x) as a Composition of F, G f(x)=x2+6g(x)=−2xh(x)=x−4F(x)=−2x−4\begin{array} { l } f ( x ) = x ^ { 2 } + 6 \quad g ( x ) = - 2 x \quad h ( x ) = \sqrt { x - 4 } \\F ( x ) = \sqrt { - 2 x - 4 }\end{array}f(x)=x2+6g(x)=−2xh(x)=x−4​F(x)=−2x−4​​

Write the Function F(x) as a Composition of F, G $\begin{array} { l } f ( x ) = x ^ { 2 } + 6 \quad g ( x ) = - 2 x \quad h ( x ) = \sqrt { x - 4 } \\F ( x ) = \sqrt { - 2 x - 4 }\end{array}$