Problem 3-6 (Iterated functions)

Table[Nest[f,n,i],{i,0,5}]

star[f_,c_,n_]:=Length[NestWhileList[f,n,#>c&]]

f1[n_]:=n-1
f2[n_]:=n/2
f3[n_]:=N[Sqrt[n]]