Answer
On $[0,2]$: $f(x)$
On $(6,\infty)$: $f(x)$
Work Step by Step
We are given the functions:
$f(x)=3x+2$
$g(x)=-\sqrt{x+5}$
Determine the function $f+g$:
$(f+g)(x)=f(x)+g(x)=3x+2-\sqrt{x+5}=3x-\sqrt{x+5}+2$
Graph the functions $f$, $g$ and $f+g$:
On the interval $[0,2]$, $f(x)$ contributes the most to the magnitude of $f+g$.
On the interval $(6,\infty)$, $f(x)$ contributes the most to the magnitude of $f+g$.
