From my home in greater Phoenix, I am going to go out on a limb and disagree with almost everything that has been written.
A charcoal filter removes gfrit, sediment, and very small particles. A reverse osmosis filter removes even smaller particles. Neither will remove dissolved minerals. Arizona water is very hard - that is, it has a lot of dissolved minerals. To get rid of the minerals, you need a water softener, not a filter. Many Arizona houses, including mine, have one, and it is the only way to remove dissolved minerals. A whole-house water softener is fairly large - a little smaller than a refrigerator. I don't know if they are made in a size small enough to carry as a portable unit for an RV. You should call Kinnetico, the largest residential water-treatment company in the Valley area. Kinnetico's stuff is very expensive, but they will come to your house and explain it all to you if they think you might buy one. Alternatively, you could drop by the Kinnetico booth at the home shows that come to Phoenix about 4 times a year.
You can identify a water softener, as opposed to any kind of filter, by the fact that every once in a while you have to dump a bag of rock salt into a hopper. The salt DOES NOT get into the water. It is used to clean out the minerals that have been removed from the water. This cleaning cycle is automatic, and rock salt is the "soap".
A water softener will prevent any additional minerals from being deposited in your pipes and fixtures. However, nothing will remove the minerals that are already there, so you should act reasonably quickly. In my house, it took 10 years without a water softener to ruin the faucet valves and shower heads. The pipes are still adequate, thank the Lord.
By the way, an RO filter makes very clean water, but makes it extremely slowly. Unless you have a HUGE (read expensive) unit, you can't take a shower in RO water, for example - the flow rate is much too slow. The common way to use an RO filter is to put one under your kitchen sink. It slowly makes water and stores it in an accumulator tank, and you draw it out through a new separate faucet on the sink. RO water is occasionally used in the icemaker in your refrig, too, but you get the idea. You get RO water a glass at a time.
An RO filter also wastes a lot of water - for each gallon of sparkling clean RO water, the unit sends about 4 gallons down the drain. For drinking water use, you can deal with this, but for a whole-house ssytem, this would be unacceptable in most places, especially the Valley.
Good luck with all of this.
Bill