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