Write the function F(x) as a composition of f, g, or h.
-$\begin{array} { l }
f ( x ) = x ^ { 2 } - 6 \quad g ( x ) = 4 x \quad h ( x ) = \sqrt { x - 7 } \
F ( x ) = \sqrt { 4 x - 7 }
\end{array}$
A) $F ( x ) = ( g \circ h ) ( x )$
B) $F ( x ) = ( f \circ h ) ( x )$
C) $F ( x ) = ( h \circ g ) ( x )$
D) $F ( x ) = ( h \circ f ) ( x )$

Question

Write the function F(x) as a composition of f, g, or h.
-$\begin{array} { l } 
f ( x ) = x ^ { 2 } - 6 \quad g ( x ) = 4 x \quad h ( x ) = \sqrt { x - 7 } \
F ( x ) = \sqrt { 4 x - 7 }
\end{array}$
A) $F ( x ) = ( g \circ h ) ( x )$
B) $F ( x ) = ( f \circ h ) ( x )$
C) $F ( x ) = ( h \circ g ) ( x )$
D) $F ( x ) = ( h \circ f ) ( x )$

Quizplus · Accepted Answer

F(x) can be written as $h(g(x))$, where $g(x) = 4x$ is first applied to x, and then $h(x) = \sqrt{x - 7}$ is applied to the result of $g(x)$, matching the expression $\sqrt{4x - 7}$.

Write the Function F(x) as a Composition of F, G f(x)=x2−6g(x)=4xh(x)=x−7F(x)=4x−7\begin{array} { l } f ( x ) = x ^ { 2 } - 6 \quad g ( x ) = 4 x \quad h ( x ) = \sqrt { x - 7 } \\F ( x ) = \sqrt { 4 x - 7 }\end{array}f(x)=x2−6g(x)=4xh(x)=x−7​F(x)=4x−7​​

Write the Function F(x) as a Composition of F, G $\begin{array} { l } f ( x ) = x ^ { 2 } - 6 \quad g ( x ) = 4 x \quad h ( x ) = \sqrt { x - 7 } \\F ( x ) = \sqrt { 4 x - 7 }\end{array}$