The domain of a function is the set of all the points (or x values) where the function exists.
The graph of the function f only exists for values of x between 2 and 11 (both inclusive), thus the domain of f is [2,11].
The function g exists only for values of x between 1 and 9, thus the domain of g is [1,9].
The function f + g exists only where f exists AND g exists. Thus, the domain of f + g is [2,9]