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Question 4.4: Determining whether a system is homogeneous Test, for homoge......

Determining whether a system is homogeneous

Test, for homogeneity, the system whose input-output relationship is

y(t) = exp(x(t))

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Let x_1(t) = g(t).   Then y_1(t) = exp(g(t)).   Let x_2 (t) = K g(t).   Then y_2(t) = exp(K g(t)) = [exp(g(t))]^K ≠ K y_1(t). Therefore this system is not homogeneous.

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