Problem 2
Although not difficult but I find these kind of problems the most confusing.
Now we were asked to check whether the system defined by the equation $ y(t) = x(1-t) $ is time-invariant or not?
One easy approach would be as follows
Now
$ x(1-t) = x (-t+1)) $
$ x(t) $ ⇒ DELAY ⇒ $ x(t-to) $ ⇒ SYSTEM ⇒ $ x (-t-to+1))= x(1-t-to) $
And,
$ x(t) $ ⇒ SYSTEM ⇒ $ x(-t +1 ) $ ⇒ DELAY ⇒ $ x (-(t-to)+1))=x(1-t+to) $
These two outputs are not the same and hence the above system is not linear time invariant
