Use function notation to write $g$ in terms of $f ( x ) = x ^ { 3 }$.
$$g ( x ) = - \frac { 1 } { 5 } ( x + 4 ) ^ { 3 }$$
A) $\quad g ( x ) = - \frac { 1 } { 5 } [ f ( x ) ] ^ { 3 } + 4$
B) $g ( x ) = - \frac { 1 } { 5 } [ f ( x ) + 4 ]$
C) $g ( x ) = - [ f ( x ) ] ^ { 3 } + \frac { 64 } { 5 }$
D) $\quad g ( x ) = - \frac { 1 } { 5 } [ f ( x ) ] ^ { 3 } + 64$
E) $\quad g ( x ) = - \frac { 1 } { 5 } [ f ( x + 4 ) ]$

Question

Quizplus · Accepted Answer

Given $f(x) = x^3$, $g(x) = -\frac{1}{5}(x + 4)^3$ can be rewritten using $f$ by substituting $x + 4$ into $f$, resulting in $g(x) = -\frac{1}{5}f(x + 4)$, 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 $f ( x ) = x ^ { 3 }$