The inverted pre-outs have two intended purposes. The most simple purpose, which can be used even with just one amp and one pair of speakers, is to invert one of the channels as it passes through the amp, and then fix it again by inverting the speaker wires on that same channel. That means content that is the same on both channels (usually Bass) will hit the opposite voltage rails of the amp (positive
and negative) instead of the same voltage rail as it passes through the amp.
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The other purpose is to be able to bridge amps. This works great for amps that don't have a built-in ability to be bridged, and works on pretty much any amplifier that has a common ground.
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If your subwoofer and your mains overlap in terms of frequency response, and they are out of phase with each other, they could potentially cancel out each other's bass. Most subwoofers either have an invert switch or even better, an adjustable phase knob, to be able to solve this problem. In the absence of this switch or knob, the inverted pre-outs on the yamaha could be used to invert the polarity of your sub relative to your mains. I have to say though, for a sub to not have this built-in... doesn't reflect well on the subwoofer.