The Laplace transform of the function f(t) = δ(t2

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The Laplace transform of the function
f(t) = δ(t² – 3t + 2)

1. e^{– s} + e^{– 2s}
2. e^s + e^2s
3. e^{– s} + e^2s
4. e^s + e^{– 2s}

Correct Option: A

The given impulse function is
f(t) = δ(t² – 3t² + 2)
= δ[(t – 1) (t – 1)]
= δ(t – 1) u(t – 1) + δ(t – 2) u(t – 2)
Therefore, Laplace transform of
L{δ(t – 1)t + δ(t – 2)} = e^{– s} + e^{– 2s}
Hence, alternative (A) is the correct choice.