What is laplacetransform 1-2e^{-4t} ?

The answer to laplacetransform 1-2e^{-4t} is 1/s-2/(s+4)

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laplacetransform 1-2e^{-4t}

laplace transform

1 - 2 e^{- 4 t}

\frac{1}{s} - \frac{2}{s + 4}

Solution steps

L {1 - 2 e^{- 4 t}}

Use the linearity property of Laplace Transform:

For functions

f (t), g (t)

and constants

a, b : L {a \cdot f (t) + b \cdot g (t)} = a \cdot L {f (t)} + b \cdot L {g (t)}

= L {1} - 2 L {e^{- 4 t}}

L {1} : \frac{1}{s}

L {e^{- 4 t}} : \frac{1}{s + 4}

= \frac{1}{s} - 2 \cdot \frac{1}{s + 4}

Refine

\frac{1}{s} - 2 \frac{1}{s + 4} : \frac{1}{s} - \frac{2}{s + 4}

= \frac{1}{s} - \frac{2}{s + 4}

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What is laplacetransform 1-2e^{-4t} ?
The answer to laplacetransform 1-2e^{-4t} is 1/s-2/(s+4)