Maybe something like this?
NamesDefaultToHere(1);
// Sample data
dt = Open("$SAMPLE_DATA/Nonlinear Examples/Negative Exponential.jmp");
// Fit a plausible model, and do inverse prediction for Y = 0.8 and 0.9
fc = dt << Fit Curve(Y( :Y ), X( :X ), Fit Logistic 2P(Custom Inverse Prediction( Response( {0.8, 0.9} ))));
// Get the inverse predictions into a table
dtp = Report(fc)[TableBox(4)] << makeDataTable;