What is inverse oflaplace F(s)= 7/(4s-12) ?

The answer to inverse oflaplace F(s)= 7/(4s-12) is 7/4 e^{3t}

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inverse oflaplace F(s)= 7/(4s-12)

inverse laplace

F (s) = \frac{7}{4 s - 12}

\frac{7}{4} e^{3 t}

Solution steps

L^{- 1} {\frac{7}{4 s - 12}}

= L^{- 1} {\frac{7}{4} \cdot \frac{1}{s - 3}}

Use the constant multiplication property of Inverse Laplace Transform:

For function

f (t)

and constant

a : L^{- 1} {a \cdot f (t)} = a \cdot L^{- 1} {f (t)}

= \frac{7}{4} L^{- 1} {\frac{1}{s - 3}}

Use Inverse Laplace Transform table:

L^{- 1} {\frac{1}{s - a}} = e^{a t}

L^{- 1} {\frac{1}{s - 3}} = e^{3 t}

= \frac{7}{4} e^{3 t}

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What is inverse oflaplace F(s)= 7/(4s-12) ?
The answer to inverse oflaplace F(s)= 7/(4s-12) is 7/4 e^{3t}