How to find the range of $f(t)=e^{-3t} \sin{(2t)}+e^{t/2}t^{7/2}+\sin(t/2)$?

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I need to find the range of these functions


$a)f(t)=e^{-3t} \sin{(2t)}+e^{t/2}t^{7/2}+\sin(t/2)$

$b)f(t)=\sin^{2}3t$


It is from a laplace transform and app. homework. So I thought it is about laplace transform. But I couldnt correlate.

i.e. laplace transform of second function is $\frac{18}{(s^3 + 36 s)}$. although the range of $f(t)=\sin^{2}3t$ is ${ 0\leq y\leq1}$, range of the transform is $y\in R$. What does this have to do with laplace transform? thanks.