Write the function F(x) as a composition of f, g, or h.
-$$\begin{array} { l }
f ( x ) = x ^ { 2 } - 1 \quad g ( x ) = - 4 x \quad h ( x ) = \sqrt { x - 2 } \
F ( x ) = \sqrt { x ^ { 2 } - 3 }
\end{array}$$
A) $\mathrm { F } ( \mathrm { x } ) = ( \mathrm { h } \circ \mathrm { f } ) ( \mathrm { x } )$
B) $F ( x ) = ( h \circ g ) ( x )$
C) $\mathrm { F } ( \mathrm { x } ) = ( \mathrm { g } \circ \mathrm { h } ) ( \mathrm { x } )$
D) $F ( x ) = ( f \circ h ) ( x )$

Question

Write the function F(x) as a composition of f, g, or h.
-$$\begin{array} { l } 
f ( x ) = x ^ { 2 } - 1 \quad g ( x ) = - 4 x \quad h ( x ) = \sqrt { x - 2 } \
F ( x ) = \sqrt { x ^ { 2 } - 3 }
\end{array}$$
A) $\mathrm { F } ( \mathrm { x } ) = ( \mathrm { h } \circ \mathrm { f } ) ( \mathrm { x } )$
B) $F ( x ) = ( h \circ g ) ( x )$
C) $\mathrm { F } ( \mathrm { x } ) = ( \mathrm { g } \circ \mathrm { h } ) ( \mathrm { x } )$
D) $F ( x ) = ( f \circ h ) ( x )$

Quizplus · Accepted Answer

$F(x) = \sqrt{x^2 - 3}$ can be rewritten as $\sqrt{x^2 - 1 - 2}$, which is $\sqrt{f(x) - 2}$, or $h(f(x))$, matching option A: $F(x) = (h \circ f)(x)$.

Write the Function F(x) as a Composition of F, G f(x)=x2−1g(x)=−4xh(x)=x−2F(x)=x2−3\begin{array} { l } f ( x ) = x ^ { 2 } - 1 \quad g ( x ) = - 4 x \quad h ( x ) = \sqrt { x - 2 } \\F ( x ) = \sqrt { x ^ { 2 } - 3 }\end{array}f(x)=x2−1g(x)=−4xh(x)=x−2​F(x)=x2−3​​

Write the Function F(x) as a Composition of F, G $\begin{array} { l } f ( x ) = x ^ { 2 } - 1 \quad g ( x ) = - 4 x \quad h ( x ) = \sqrt { x - 2 } \\F ( x ) = \sqrt { x ^ { 2 } - 3 }\end{array}$