System invertability Can someone please explain how to determine if a system is invertible or not. The particular systems that I am looking at are:

$y(t) = \cos \left( x(t) \right)$ - I believe this is non-invertable because of the periodic function

$y[n] = nx[n]$ - I think this is invertable and the inverse is $x[n]/n$ 

$y[n] = x[4n + 1]$ - Is the inverse $x[1/4n - 1]$?

$y[n] = x[n - 2] - 2x[n - 8]$ - I do not know even how to begin

I am really confused with systems... did not understand a single thing in the lecture today, and now reading the book ("Signals and Systems", Oppenheim) I am getting frustrated. Is there an algebraic procedure for determining the inverse of a system?

Please help.
$$ y[n] = x[n-2] - 2 x[x-8] $$

that's actually a linear and time-invariant system.  you invert it by computing the Z transform

$$ Y(z) = z^{-2}X(z) - 2 z^{-8}X(z) $$

solve for $X(z)$, then inverse Z transform.  you might find out that, to invert this system, you will have to look at future samples, so the inverse would not be causal.