Question

The system y(t)  = x^2(t) 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 got this question in final exam.

The query is from Characterization and Nature of Systems in division Laplace Transform and System Design of Signals and Systems

Answer 1

Correct answer is (d) Not invertible

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

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

Let, x (t) = -u (t), then y (t) = {-u (t)}^2 = u (t)

Thus different inputs leads to same output hence system is non-invertible.