In[]:=
InverseFunction[b1/(1+E^(c1(#-a1)))&]
InverseFunction
:Inverse functions are being used. Values may be lost for multivalued inverses.
Out[]=
a1c1-Log
#1
b1-#1

c1
&
In[]:=
InverseFunction[b1/(1+E^(c1(#-a1)))+b2/(1+E^(c2(#-a2)))&]
Out[]=
InverseFunction
b1
1+
c1(#1-a1)

+
b2
1+
c2(#1-a2)

&