Are the modem and the codec functional inverses ie could an inverted modem?

No, the modem and codec are not exactly the functional inverse of each other.

teh modem converts the digital data to analog signal by teh modulating part of it.

teh demodulating part of the modem can be used to covert teh ANALOG SIGNAL to digital data....but this analog signal will be modulated analog signal.

the coding part of teh codec convert teh analog signals to teh digital signal .these analog signals are pure analog signals.

Hence teh codec and modem may seem as functional inverses but do not work as so due to teh fact dat the demodulating part of the modem used only the modulated analog signal and cannot process the pure analog signals .