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While studying Laplace Transform i found that region of convergence (ROC) is important because for some problems we have same Laplace Transform but different ROC helps us to take correct inverse Laplace Transform. So, Now i am practicing inverse Laplace Transform problem i found almost every probelm to find $x(t)$ is without ROC. So i want to ask that without have ROC how can we solve inverse Laplace Transform?

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Strictly speaking you can't because without specifying the ROC, the inverse Laplace transform is generally not unique. However, in many contexts there is the implicit assumption of causality of the corresponding time function (i.e., $x(t)=0$ for $t<0$), which is equivalent to stating that the ROC is a right half-plane.

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  • $\begingroup$ We can say that every system is casual if it is defined for t>0? $\endgroup$ – Aadnan Farooq A Dec 2 '15 at 4:19

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