Question

The system y(t)  = x(2t) is ______________

(a) Invertible with input x(t) and output y(t)

(b) Invertible with input x(t)

(c) Invertible with output y(t)

(d) Not invertible

I had been asked this question by my college director while I was bunking the class.

This intriguing question originated from Characterization and Nature of Systems in chapter Laplace Transform and System Design of Signals and Systems

Answer 1

Right answer is (a) Invertible with input x(t) and output y(t)

The explanation: Given y (t) = x (2t)

Let x (t) = u (t), then y (t) = u (2t) = u (t)

Let, x (t) = -u (t), then y (t) = – u (2t) = – u (t)

Since different inputs leads to different outputs hence system is invertible with both input x (t) and output y (t).