Do you live in California? If not, I have no idea what law applies to you and your work.

But if you live in California you are in luck: Section 2872 of the labor code is explicit in this matter. In fact every employee assignment agreement I have handed out to someone I've hired (going back to 1989) has included the text of that section, for example:

  in accordance  with  Section  2872  of  the  California  Labor 
  Code  that  the  foregoing Agreement between you and Company does
  not require you to assign or offer to assign to Company any Invention
  that you develop entirely on your own time without using Company’s
  equipment, supplies, facilities or trade secret information, except
  for those Inventions that either: 

  a. Relate  at  the  time  of  conception  or  reduction  to
  practice to  Company’s  business,  or  actual  or demonstrably
  anticipated research or development; or

  b.Result from any work performed by you for Company. To  the
  extent  a  provision in the  foregoing  Agreement  purports
  to  require  you  to  assign an  Invention otherwise  excluded
  from  the  preceding  paragraph, the  provision  is  against
  the  public  policy  of  this  state and  is unenforceable.

  This limited exclusion does not apply to any patent or Invention
  covered  by a contract between Company and the United States
  or any of its agencies requiring full title to such patent
  or Invention to be in the United States. 

This law is widely cited as one of Silicon Valley's advantages over other places.

California went through a period of rational law making, e.g. laws like this, a presumption that drivers know what they are doing regardless of the posted speed limit, etc. Then they went insane (three strikes etc) and the rest is, sadly, history. Still not as crazy as the rest of the USA though.