Write the function F(x) as a composition of f, g, or h.
-$\begin{array} { l }
\mathrm { f } ( \mathrm { x } ) = \mathrm { x } ^ { 2 } - 8 \quad \mathrm {~g} ( \mathrm { x } ) = - 3 \mathrm { x } \quad \mathrm { h } ( \mathrm { x } ) = \sqrt { \mathrm { x } + 5 } \
\mathrm {~F} ( \mathrm { x } ) = \sqrt { \mathrm { x } ^ { 2 } - 3 }
\end{array}$
A) $\mathrm { F } ( \mathrm { x } ) = ( h \circ f ) ( \mathrm { x } )$
B) $F ( x ) = ( h \circ g ) ( x )$
C) $F ( x ) = ( f \circ h ) ( x )$
D) $\mathrm { F } ( \mathrm { x } ) = ( \mathrm { g } \circ \mathrm { h } ) ( \mathrm { x } )$

Question

Write the function F(x) as a composition of f, g, or h.
-$\begin{array} { l } 
\mathrm { f } ( \mathrm { x } ) = \mathrm { x } ^ { 2 } - 8 \quad \mathrm {~g} ( \mathrm { x } ) = - 3 \mathrm { x } \quad \mathrm { h } ( \mathrm { x } ) = \sqrt { \mathrm { x } + 5 } \
\mathrm {~F} ( \mathrm { x } ) = \sqrt { \mathrm { x } ^ { 2 } - 3 }
\end{array}$
A) $\mathrm { F } ( \mathrm { x } ) = ( h \circ f ) ( \mathrm { x } )$
B) $F ( x ) = ( h \circ g ) ( x )$
C) $F ( x ) = ( f \circ h ) ( x )$
D) $\mathrm { F } ( \mathrm { x } ) = ( \mathrm { g } \circ \mathrm { h } ) ( \mathrm { x } )$

Quizplus · Accepted Answer

$F(x) = \sqrt{x^2 - 3}$ can be rewritten as $\sqrt{x^2 - 8 + 5}$, which corresponds to applying $h$ to $f(x) = x^2 - 8$, hence $F(x) = (h \circ f)(x)$.

Write the Function F(x) as a Composition of F, G