Can a Ph.D student change his adviser, if he is supported by a Research Assistantship by the adviser upon admission (and possibly first year)? According to my offer, I am admitted to the Ph.D program and funded by a Research Assistantship by Professor X. Nevertheless, I am interested in other research directions, and we are supposed to decide our adviser by the end of the first semester.

Is it appropriate to change adviser in my case, as I am funded by Professor X?
It is usually possible, but plan for two things to happen:


[Almost certain] You will lose this RA-stipend. RAs are usually in the context of specific projects and under the supervision of specific advisors, so when you decide to work on an entirely different project with a different position (which is typically your right as a PhD student) you become ineligible to be funded in this way. You need to understand that most RAs come from projects, where a PI has promised to a funding agency or company that a certain project will be delivered within a time frame. If you then decide to work on something else, the PI needs to find another person to actually do the work that has been promised. Note that this does not necessarily mean that you won't have a stipend anymore, but it will likely need to be a different source (e.g., either a TA position or an RA sponsored 
by your new advisor).
[Possible] There may be some fallout with the PI sponsoring the RA. I guess most people can accept that sometimes the first year shows that you are not an ideal fit and switching advisors is the best solution for everybody, but planning to switch all along when accepting the offer may understandably lead to some bad blood. In essence, you are trying to milk a year of funding out of a project you have no intention of actually contributing to long-term. Many people will find this highly disagreeable.