Answer
On $[0,2]$: $f(x)$
On $(6,\infty)$: $g(x)$
Work Step by Step
We are given the functions:
$f(x)=3x$
$g(x)=-\dfrac{x^3}{10}$
Determine the function $f+g$:
$(f+g)(x)=f(x)+g(x)=3x-\dfrac{x^3}{10}$
Graph the functions $f$, $g$ and $f+g$:
On the interval $[0,2]$, $f(x)$ contributes to most of the magnitude of $(f+g)(x)$.
On the interval $(6,\infty)$, $g(x)$ contributes to most of the magnitude of $(f+g)(x)$.
