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InverseFunction returning working function or just a symbol

Hi all,
I am puzzled by the following behavior (focus on the end, the rest is only to provide context):

In[88]:= u[c_,l_]:=Log[c]-Log[1+l^(1+k)/(1+k)]
In[14]:= T[z_]:=(1-0.84/1.3) * z
In[103]:= umaxType[n_]:=MaxValue[{u[n l-T[n l],l],l>=0},l]
In[101]:= lType[n_]:=ArgMax[{u[n l-T[n l],l],l>=0},l]
In[105]:= zType[n_] := n lType[n]
In[111]:= Type := InverseFunction[zType]
In[134]:= Type[5345]
Out[134]= 5030.99
In[136]:= Type[2]
Out[136]= (zType^(-1))[2]
In[137]:= Type[4324424]
Out[137]= (zType^(-1))[4324424]

I understand that there could be many justified reasons why the inversion might not work for a specific argument. Still, I am deeply puzzled that sometimes I receive back a symbol that nothing else is able to do anything about (why not an error message, then?), sometimes a number. How could this be improved?


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