[R] Problem with fitted.value function

[AC]

Who can help me in finding the right fitted-value-function?Based upon a
linear model (2-dimensional, 1 result-variable and 1 input-variable).
I found the perfect regression model (not always simply linear) by the
function lm(). Based on the given input and output tuples. For these exact
 input values I can get the exact fitted values by the function
 fitted.values.
The problem is, once I want to extrapolate with the automaticly found
 function (not always the same) and new input-variables I don't know how to
 calculate automaticly the fitted values. I don't know how to use the fitted
 values function with a given function and given input-variables but yet 
unknown result-values.

 Who can help me get the right fitted value function and tell me how to use 
it.

 Thanks in advance for any help.