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The Laplace transform of x(t) is .  Then Laplace transform of e−6tx(t) is :

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Option 1 :
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The correct option is 1

Concept:

If the Laplace transform of a function \( x(t) \) is known, then the Laplace transform of \( e^{-at}x(t) \) can be obtained using the time-shifting property of the Laplace transform.

This property states that:

, where \( X(s) = \mathcal{L}\{x(t)\} \)

Given:

Calculation:

We are asked to find the Laplace transform of \( e^{-6t}x(t) \).

Using the time-shifting property:

 

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