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Recently I read that raw audio (uncompressed WAVE files) are stored in LPCM (Linear Pulse Code Modulation) encoded format. Now I believe that the LPCM encoding stores basically the waveform which the recorder receives, which is basically a superposition of several frequencies that were present during the recording.

Now we all know that any standard music player (say Windows Media Player) gives us an equalizer which can boost or dampen frequency bands. I know that we can get the amount of a component frequency from a complex waveform by using Fourier transform, however to use Fourier transform we require the function of the waveform. However, the function is not available in the LPCM encoded stream, only the waveform.

So my question is how exactly does this equalizing work in software equalizers?

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However, the function is not available in the LPCM encoded stream, only the waveform.

They're the same thing. The "function" is just a mapping from time to value. The waveform is just a mapping from time to value.

You can find more details here.