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

Question

Quizplus · Accepted Answer

Given $f(x) = x^3$, $g(x)$ can be written in terms of $f$ by substituting $x+9$ for $x$ in $f(x)$ and then multiplying the result by $-\frac{1}{2}$, which matches option 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 $f ( x ) = x ^ { 3 }$