If you cook carrots, some long-chain carbohydrates
are broken down to
fructose and glucose, so cooked carrots may be sweat, while raw ones are usually not. So, in general, yes, it's posible that F/G ratio changes during cooking or drying.
Also, bananas are typical fruit well tolerated by many with FM. If you can't tolerate bananas, it means, there may be something other in bananas what irritates you. It's also a big difference between riped and green bananas...