# The system y(t) = $\frac{d x(t)}{dt}$ is ______________

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The system y(t)  = $\frac{d x(t)}{dt}$ 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

The question was posed to me in an international level competition.

My enquiry is from Characterization and Nature of Systems in chapter Laplace Transform and System Design of Signals and Systems

by (42.1k points)
Right option is (d) Not invertible

Explanation: Given y (t) = $\frac{d x(t)}{dt}$

Let x (t) = 1, then y (t) = 0

Let, x (t) = 2, then y (t) = 0

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

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