What is inverse oflaplace f(t)=7t+3 ?

The answer to inverse oflaplace f(t)=7t+3 is 7\delta'(t)+3\delta(t)

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inverse oflaplace f(t)=7t+3

inverse laplace

f (t) = 7 t + 3

7 δ' (t) + 3 δ (t)

Solution steps

L^{- 1} {7 t + 3}

Use the linearity property of Inverse Laplace Transform:

For functions

f (s), g (s)

and constants

a, b : L^{- 1} {a \cdot f (s) + b \cdot g (s)} = a \cdot L^{- 1} {f (s)} + b \cdot L^{- 1} {g (s)}

= 7 L^{- 1} {t} + L^{- 1} {3}

L^{- 1} {t} : δ^{'} (t)

L^{- 1} {3} : 3 δ (t)

= 7 δ^{^{'}} (t) + 3 δ (t)

What is inverse oflaplace f(t)=7t+3 ?
The answer to inverse oflaplace f(t)=7t+3 is 7\delta'(t)+3\delta(t)