We propose to calculate inelastic response functions from the inversio
n of their integral transform with a Lorentz kernel. The transform can
be obtained using bound-state type methods. Thus one does not need to
solve the much more complicated continuum problem with many open chan
nels. Contrary to other integral transforms considered in the literatu
re, the inversion leads to results of excellent accuracy and stability
. This is explicitly shown for the longitudinal deuteron response.