My doctor prescribed me xanax (alprazolam) for depression/anxiety. is that effective?

Depends on what you: mean by effective. Xanax (alprazolam) will reduce anxiety short-term, but does not really have any significant beneficial effect on depression. Like other benzodiazepines, Xanax (alprazolam) causes physical dependency and tolerance, with a requirement for more and more medication, doing less and less over time. Antidepressant medications and psychotherapy are better ways to treat both conditions. Best if used short-term.