I don't understand why my book is saying that this system is not invertible. y(t) = cos(x(t)) ? Wouldn't, arccos{ y(t) } = x(t) and therefore be an inverse system?
First check on what your book says the definition of invertible is. What about times T1 and T2, where T1 and T2 are different x(T1) = 0, x(T2)= 2PI y(T1) = 1 and y(T2)=1 Suppose y(t)=1 what is the value of t?