Answer
$(-\infty,+\infty)$
Work Step by Step
$f(x)*g(x)=(x^2+4x)(2-x)=2x^2-x^3+8x-4x^2=-2x^2-x^3+8x$ the domain is all $\mathbf{R}$
$(-\infty,+\infty)$
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