GATE 2025 PI – Question 13

Engineering Mathematics · Differential Equations · 1 mark · Multiple choice

If F(s) is the Laplace transform of f(t), find the transform of $e^{bt}f(t)$ for real constant b.

$F(s-b)$
$F(s+b)$
$-F(s)$
$F(b-s)$

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Show answer and explanation

Correct answer: (A) $F(s-b)$

Explanation

In the defining integral, $e^{-st}e^{bt}f(t)=e^{-(s-b)t}f(t)$. The transform is therefore **F(s−b), A**, with the corresponding shift of convergence region.

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