Gianna Johnson

2023-04-01

The Laplace transform of the product of two functions is the product of the Laplace transforms of each given function. True or False

Joselyn Arias

The statement The statement The Laplace transform of the product of two functions is the product of the Laplace transforms of each given function is False.
In general, the Laplace transform of a product of two functions does not equal the product of their individual Laplace transforms.
Mathematically, let's consider two functions $f\left(t\right)$ and $g\left(t\right)$. The Laplace transform of their product, denoted as $ℒ\left[f\left(t\right)·g\left(t\right)\right]$, is not equal to $ℒ\left[f\left(t\right)\right]·ℒ\left[g\left(t\right)\right]$.
The Laplace transform of a product involves convolution, which is a different operation than simply multiplying the Laplace transforms of individual functions.
Therefore, the statement is false, and the Laplace transform of the product of two functions is generally not equal to the product of their individual Laplace transforms.

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