Can I use inverse of the same function when defining the function itself? For example : b[x_]:=1+Integrate[InverseFunction[b][a],{a,0,x}] b[5] Typing that in I get an error: $RecursionLimit::reclim: Recursion depth of 256 exceeded.

A simpler example: b[x_] := 1 + InverseFunction[b][x] b[5] also gives me the same error.

I understand that it has to do with the fact that a function has its own inverse in its definition, which is not easy to solve (maybe not possible?)

Could you please give me some advice on what to do in the case that I want to solve a problem of this type (my actual problem is more complicated, but I wanted to know on the simpler example).

Are there any other ways to get a solution for this type of problem?

I'm new to Mathematica, so I'm sorry if I'm making some trivial mistakes, all the help would be very appreciated. I'm looking forward to your reply, thank you in advance!