Write the function F(x) as a composition of f, g, or h.
-$\begin{array} { l }
f ( x ) = x ^ { 2 } - 6 \quad g ( x ) = - 5 x \quad h ( x ) = \sqrt { x + 5 } \
F ( x ) = - 5 x ^ { 2 } + 30
\end{array}$
A) $F ( x ) = ( g \circ f ) ( x )$
B) $F ( x ) = ( h \circ g ) ( x )$
C) $F ( x ) = ( f \circ g ) ( x )$
D) $F ( x ) = ( g \circ h ) ( x )$

Question

Write the function F(x) as a composition of f, g, or h.
-$\begin{array} { l } 
f ( x ) = x ^ { 2 } - 6 \quad g ( x ) = - 5 x \quad h ( x ) = \sqrt { x + 5 } \
F ( x ) = - 5 x ^ { 2 } + 30
\end{array}$
A) $F ( x ) = ( g \circ f ) ( x )$
B) $F ( x ) = ( h \circ g ) ( x )$
C) $F ( x ) = ( f \circ g ) ( x )$
D) $F ( x ) = ( g \circ h ) ( x )$

Quizplus · Accepted Answer

F(x) can be rewritten as -5(x^2 - 6), which matches the composition of g(f(x)), where f(x) = x^2 - 6 and g(x) = -5x.

Write the Function F(x) as a Composition of F, G f(x)=x2−6g(x)=−5xh(x)=x+5F(x)=−5x2+30\begin{array} { l } f ( x ) = x ^ { 2 } - 6 \quad g ( x ) = - 5 x \quad h ( x ) = \sqrt { x + 5 } \\F ( x ) = - 5 x ^ { 2 } + 30\end{array}f(x)=x2−6g(x)=−5xh(x)=x+5​F(x)=−5x2+30​

Write the Function F(x) as a Composition of F, G $\begin{array} { l } f ( x ) = x ^ { 2 } - 6 \quad g ( x ) = - 5 x \quad h ( x ) = \sqrt { x + 5 } \\F ( x ) = - 5 x ^ { 2 } + 30\end{array}$