actually the STL can do this without much code, I advise you learn a bit about the STL because it lets you do some fancy things, anyways this is what I use.
std::string GetFileExtension(const std::string& FileName)
{
if(FileName.find_last_of(".") != std::string::npos)
return FileName.substr(FileName.find_last_of(".")+1);
return "";
}
this solution will always return the extension even on strings like "this.a.b.c.d.e.s.mp3" if it cannot find the extension it will return "".