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