The composition of the logit function and its inverse is not numerically invariant with respect to the decimal place

I have defined the following two functions:

logit[x_] : = Module[{},
   Log[x/(1 - x)]
   ];
invLogit[x_] : = Module[{},
   E^x/(1 + E^x)
   ];

One is the reverse of the other. however,

In[37]: = logit[invLogit[34.55555]]Outside[37]= 34.6574

Is it possible to increase the accuracy of calculations?