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I suppose it depends what the filter is actually filtering. Very hard water requires quite specific filtering to be really good for coffee machines. Might be worth getting a test kit (from BWT or similar) and seeing what goes in Vs what comes out, however I'd prefer to have the water treated before it hits the machine at all.
Some people use mineral waters, some people filter their mains and use that.
Yeah it's the tank on the back of the machine, which has a filter in that I change every 3 months. It's not plumbed into the mains