If $$x\left[ N \right] = {\left( {1/3} \right)^{\left| n \right|}} - {\left( {1/2} \right)^n}\,u\left[ n \right],$$ then the region of convergence $$(ROC)$$ of its $$Z$$-transform in the $$Z$$-plane will be

The unilateral Laplace transform of $$f(t)$$ is
$$\,{1 \over {{s^2} + s + 1}}.$$ The unilateral Laplace transform of $$t$$ $$f(t)$$ is

$$u(t)$$ represents the unit step function. The Laplace transform of $$u\left( {t - \tau } \right)$$ is

The laplace transform of a function $$f(t)$$ is defined by
$$F\left( s \right) = L\left\{ {f\left( t \right)} \right\} = \int\limits_0^\infty {{e^{ - st}}f\left( t \right)dt.} $$.
Find the inverse laplace transform of $$F(s-a)$$