Correct Answer - Option 3 : F(s + a)
Concept:
The Laplace transform F(s) of a function f(t) is defined by:
\(L\text{(}f\left( t \right)\text{ }\!\!\}\!\!\text{ }=F\left( s \right)=\underset{0}{\overset{\infty }{\mathop \int }}\,{{e}^{-st}}f\left( t \right)dt\)
The time-shifting property of Laplace transform:
\(L\left\{ f\left( t-a \right) \right\}={{e}^{-as}}F\left( s \right)\)
\(L\left\{ f\left( t+a \right) \right\}={{e}^{as}}F\left( s \right)\)
Shifting in the frequency domain:
\({e^{at}}f\left( t \right) \leftrightarrow F\left( {s - a} \right)\)
\({e^{-at}}f\left( t \right) \leftrightarrow F\left( {s + a} \right)\)
Application:
L{f(t)} = F(s)
L[e-at f(t)] = \(F(s+a)\)
