[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.