Summary: When we are manipulating functions with computer programs, especially with computer algebra systems, we easily find ourselves confronted with the problem of modifying the range and the domain of a function with our program. If the underlying spaces are topological or even more, finite dimensional Euclidean spaces, the domains and ranges are mostly topologically simple, i.e. closed, compact, or open sets. If the space is one dimensional, the simplest case is that, the sets are intervals. In numerical computations one of the classic methods is interval analysis or interval arithmetics, but this method uses closed intervals and is mainly interested in numerical accuracy. We care mostly about open sets and the numerical precision is not too important. In this article we treat this by modifying the method, to manipulate arbitrary intervals symbolically, and we solve this problem in the computer algebra system Maple.