Use function notation to write $g$ in terms of $f ( x ) = x ^ { 3 }$.
$g ( x ) = - \frac { 1 } { 2 } ( x + 9 ) ^ { 3 }$
A) $g ( x ) = - \frac { 1 } { 2 } [ f ( x ) ] ^ { 3 } + 9$
B) $g ( x ) = - \frac { 1 } { 2 } [ f ( x ) + 9 ]$
C) $\quad g ( x ) = - [ f ( x ) ] ^ { 3 } + \frac { 729 } { 2 }$
D) $g ( x ) = - \frac { 1 } { 2 } [ f ( x ) ] ^ { 3 } + 729$
E) $\quad g ( x ) = - \frac { 1 } { 2 } [ f ( x + 9 ) ]$

Question

Quizplus · Accepted Answer

Given $f(x) = x^3$, $g(x) = -\frac{1}{2}(x + 9)^3$ can be rewritten using $f$ by substituting $x + 9$ into $f$, resulting in $g(x) = -\frac{1}{2}f(x + 9)$, which matches choice E.

Use Function Notation to Write ggg In Terms Of f(x)=x3f ( x ) = x ^ { 3 }f(x)=x3

Use Function Notation to Write $g$ In Terms Of $f ( x ) = x ^ { 3 }$