Transform function in terms of Heaviside functions.

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I am working on the red-shaded problem below however I am unsure how to use my answer from part b to answer the question. Any help is appreciated.

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Well, $Y(s) = H(s) * F(s)$.

So then the response $y(t)$ can be determined by inverting $Y(s) = H(s) * F(s) = H(s) * U(s) $, where $ U(s) $ is the Laplace Transform of the Heaviside function.