Question

If f(t)=f1(t)+f2(t), the laplace transform of f(t) exists if f1(t) and f2(t) does not have the same R.O.C.

(a) True

(b) False

I had been asked this question in an interview for internship.

This intriguing question comes from Laplace Transform in portion Control System Applications of MATLAB

Answer 1

Right choice is (b) False

The best explanation: If the functions f1(t) and f2(t) do not have the same R.O.C., the laplace transform of f(t) won’t exist. This is because f(t) is a result of addition of both the function and if one of them doesn’t exist, the entire function would collapse.