Final answer:
To find the Fourier transform of the given signal x(t)=e^(-t), substitute the signal into the formula for the Fourier transform and solve for F(w).
Step-by-step explanation:
The Fourier transform of the given continuous-time signal x(t)=e^(-t) can be found using the formula:
F(w) = ∫ x(t)e^(-jwt)dt
Substituting the given signal into the formula:
F(w) = ∫ e^(-t)e^(-jwt)dt
Simplifying the expression:
F(w) = ∫ e^((-1-jw)t)dt
Integrating this expression and solving for F(w) will give the Fourier transform of the signal x(t).