Write the function F(x) as a composition of f, g, or h.
-$\begin{array} { l }
f ( x ) = x ^ { 2 } - 2 \quad g ( x ) = - 6 x \quad h ( x ) = \sqrt { x - 1 } \
F ( x ) = 36 x ^ { 2 } - 2
\end{array}$
A) $F ( x ) = ( g \circ f ) ( x )$
B) $F ( x ) = ( g \circ h ) ( x )$
C) $F ( x ) = ( f \circ g ) ( x )$
D) $F ( x ) = ( h \circ g ) ( x )$

Question

Write the function F(x) as a composition of f, g, or h.
-$\begin{array} { l } 
f ( x ) = x ^ { 2 } - 2 \quad g ( x ) = - 6 x \quad h ( x ) = \sqrt { x - 1 } \
F ( x ) = 36 x ^ { 2 } - 2
\end{array}$
A) $F ( x ) = ( g \circ f ) ( x )$
B) $F ( x ) = ( g \circ h ) ( x )$
C) $F ( x ) = ( f \circ g ) ( x )$
D) $F ( x ) = ( h \circ g ) ( x )$

Quizplus · Accepted Answer

F(x) can be obtained by first applying g(x) = -6x to x, and then applying f to the result, which squares the result of g(x) and subtracts 2. This matches the definition of composition (f ∘ g)(x).

Write the Function F(x) as a Composition of F, G f(x)=x2−2g(x)=−6xh(x)=x−1F(x)=36x2−2\begin{array} { l } f ( x ) = x ^ { 2 } - 2 \quad g ( x ) = - 6 x \quad h ( x ) = \sqrt { x - 1 } \\F ( x ) = 36 x ^ { 2 } - 2\end{array}f(x)=x2−2g(x)=−6xh(x)=x−1​F(x)=36x2−2​

Write the Function F(x) as a Composition of F, G $\begin{array} { l } f ( x ) = x ^ { 2 } - 2 \quad g ( x ) = - 6 x \quad h ( x ) = \sqrt { x - 1 } \\F ( x ) = 36 x ^ { 2 } - 2\end{array}$