#### Answer

$f(x)=3x^{3}+x$ and $g(x)=-2x+3$

#### Work Step by Step

We know that $(f+g)(x)=f(x)+g(x)$.
Therefore, we know that the two polynomial functions will have to satisfy the following condition:
$f(x)+g(x)=3x^{3}-x+3$
Two such functions that satisfy this condition are:
$f(x)=3x^{3}+x$ and $g(x)=-2x+3$
$f(x)+g(x)=(3x^{3}+x)+(-2x+3)=3x^{3}+x-2x+3=3x^{3}-x+3$