Question

The signal x(t) and X(s) form a Laplace transform pair. If $x\left(t\right)=e^{-5t}u(-t+3)$ , then X(s) is

• A. $\frac{e^{-3(s+5)}}{s-5},Re\left[s\right]<5]$
• B. $-\frac{e^{-3(s-5)}}{s-5},Re\left[s\right]<5]$
• C. $\frac{e^{-3(s-5)}}{s-5},Re\left[s\right]<5]$
• D. $-\frac{e^{-3(s+5)}}{s+5},Re\left[s\right]<-5]$

Answer 1

The correct option is D $-\frac{e^{-3(s+5)}}{s+5},Re\left[s\right]<-5]$


$e^{5t}u\left(t\right)⟷\frac{1}{s-5}$

$e^{5(t+3)}u(t+3)⟷\frac{e^{3s}}{s-5}$

$e^{5(-t+3)}u(-t+3)⟷\frac{e^{-3s}}{-(s+5)}$

$e^{5t}u(-t+3)⟷\frac{-e^{-15}{e}^{-3s}}{s+5},Re\left[s\right]<-5$

$=\frac{-e^{-3(s+5)}}{s+5},Re\left[s\right]<-5$