If I am at x arena and I am demoted to x arena then I go in the shop and buy a chest there can I get cards from the arena I was in [duplicate]

In the shop, the chests are for the arena you are currently in (you can see it reads "arena x" for your current arena above the chest in the shop icon, see pic below)). Also, from the Clash Royale wiki shop page:

The arena number chest you can get corresponds with your current Arena.

So if you get demoted from your current highest arena, the chest will only contain cards from the current arena (not current highest) and lower.

So if you want higher arena cards, buy the chests when you are currently in that arena (but keep in mind that the chests will be more expensive, as also mentioned in the wiki).

http://clashroyalearena.com/wp-content/uploads/2016/01/clash-royale-chests-2.jpg

Note the "Arena 3" text above the chests. This photo may be slightly dated, but after just logging into the shop I can still see the text.