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Answer :
The Laplace transform of the given function f(t) = 6e^(3t) + 4e^t is F(s) = 10s / (s^2 - s - 6).
To find the Laplace transform, we substitute the expression for f(t) into the integral definition of the Laplace transform and evaluate it. The Laplace transform of e^(at) is 1 / (s - a), and the Laplace transform of a constant multiple of a function is equal to the constant multiplied by the Laplace transform of the function.
Therefore, applying these rules, we have F(s) = 6 * 1 / (s - 3) + 4 * 1 / (s - 1) = (6 / (s - 3)) + (4 / (s - 1)).
Simplifying further, we can rewrite F(s) as 10s / (s^2 - s - 6), which matches the first option provided. Hence, the correct answer is F(s) = 10s / (s^2 - s - 6).
Learn more about Laplace Transform here: brainly.in/question/20463187
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