fourier and laplace transforms

Well, I know that these transforms take a function in the -time- domain and transform it to the same function but in the -frequency- domain. Now, what does this exactly mean? One can easily interpret a wide range of meanings for a real-valued function in the time domain, such as a sine wave or a constant function. But how does one interpret the results of the complex-valued function these transforms give?

What is the exact difference between these two transforms?

What is the meaning of life?

Laplace transform

Definition:
Sf(x)e^(-xt) dx [int from x=0 to infinity] = L(f) [the laplace transform of f]

Fourier transform

Definition:
(1/sqrt(2*Pi))*Sf(k)e^(ikx) dx [int over R] = F(f) [the fourier transform of f]

yeah, that's what I asked and all...

en.wikipedia.org

Then search Laplace Transform
or Fourier Transform

Well, I can describe them in my own words..  but it'll be a paraphrase of the Wikipedia articles themselves at best..  so GTFO here and go There!

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Marijuana MUST be legalized.