Determining invertibility of a system Given a system which is either non-linear and/or time variant, Is there any systematic way to determine if this system is invertible?
For example how to determine invertibility of this system?
$$\int_{-\infty}^\infty x(5\tau)d\tau$$
In general there is no systematic way and you simply have to analyze the given system. In the case of the system in your question, it's easy to see that it can't be invertible, because the output is just a constant, namely the integral over the input function (assuming this integral exists). There are infinitely many functions which will result in the same value when integrated from $-\infty$ to $\infty$.