A CT signal x(t), which is non-zero only over the time interval, t = [-2,3] is applied to an LTIC system with impulse response h(t). The output y(t) is observed to be non-zero only over the time interval t = [-5,6]. Determine the time interval in which the impulse response h(t) of the system is possibly non-zero.
I understand how to find the output given the input and impulse response h(t) with the convolution integral either through integration or the graphical method, but I can't figure out how you can find out the impulse response given just this information. Am I just suppose to guess?