Let f:R-->Rbe a continuous function, and let = {A CR: there exists B with where are the Borel subsets of the range spaceR.Show that , the Borel subsets of the domain spaceR.

Okay, so I know f being continuous means that is open for all open v inR.

I'm not exactly sure what I need to show here. Is it just that is open inR? Then wouldn't that show it is in ? And wouldn't this be true because f inverse is open? So, all the A's in would be open. Am I on the right track? Thank you!