Help! Reverse Fourier transform of a piecewise function

I have a two-piece function in k-space that I would like to reverse
Fourier transform into r-space. The function is defined as follows:

f(k) = 4*pi*A(B^2-C^2)/((1+k^2*C^2)(1+k^2*B^2)); 0<k<k0

f(k) = 4*pi*A(B^2-C^2)*(1+k^2*C^2)/(1+k^2*B^2)*((N*k*Rb+2(N-1)*sin(k
Rb))/(N^2*k*Rb))^2; k0<k<Infinity

NB) All capital letters (A, B, C, Rb, N) are real, strictly positive
constants.

I can do the reverse transform for the first function, integrating from
zero to infinity. I realize that the second function has problems and I
am currently working on them. What I would like to know is how, in
general, do I set the limits of integration in a way that is
meaningful? And after integrating, how do I interpret and recombine the
functions in r-space?

Thanks

.

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