Answer
See below
Work Step by Step
Since, $y(s)=\dfrac{1}{2(s-2)} -\dfrac{1}{18(s+2)}-\dfrac{4}{9(s-1)}-\frac{2}{3(s-1)^2}$
The inverse Laplace transform of function can be expressed as:
$y(t)=\dfrac{1}{2(s-2)} -\dfrac{1}{18(s+2)}-\dfrac{4}{9(s-1)}-\frac{2}{3(s-1)^2}$
Now, apply the first shifting Theorem.
$f(t)= \dfrac{1}{2}e^{2t} -\dfrac{1}{18}e^{-2t}-\dfrac{4}{9}e^t-\frac{2}{3}te^t$
