Trivial Question on Fourier Transforms

[Void123]

Homework Statement

If my f(x) = {f1, f2, f3}, where each function (f1 f2 f3) is within its own domain, and I wanted to find the transform g(k), then I would be adding up three different integrals over those different limits, correct?

Homework Equations

The Attempt at a Solution

 

[HallsofIvy]

Yes.