Is carbon filtered unboiled tap water safe enough to mix with formula for 2 month old?

Depends: If you live in an area on city water& that water has an approved or superior rating it doesn't need to be boiled. As a general rule if its good enough for you to drink from the tap you can use it to mix formula. If you have rusty pipes or have other concerns about origin, gallons of filtered water are available for less than a dollar.