Combine two TF1 functions in one TF1 in a larger range

Hey rooters,
I am trying to combine two TF1 functions defined in separate ranges into a TF1 that has a larger range.
I have:
TF1* fspmu = new TF1(“fspmu”,“spmuf(x)”,L1,L2);
TF1* fmuexpo = new TF1(“fmuexpo”,“[0]*exp(-x/[1])”,L2,L3);
where L1 < L2 < L3, and I want:

TF1* fall = new TF1(“fall”, fspmu and fmuexpo, L1, L3);

My aim is to draw random numbers from a function in (L1, L3), where I have fspmu as a spline within (L1, L2) and an exponential decay fitted function fmuexpo within (L2, L3).

Any other ideas on how to implement this will be greatly appreciated. TIA