realistically no unfortunately the warrenty wont, cause the phrase that the stealers are going to hide behind is wear and tear and generally use,
You do have a good case however to go back to the
dealer you bought it from and knock some heads, if its an "approved used car" then they are supposed to have done a 102 point check which does check those things (in theory) and after all of 2 months its in need of new filters they somebody aint done their job properly
Dont expect them to roll over, they will fob you off with any excuse, it took me 2 months of aggro and in the end i had to block off the entrance of their forcourt with the car before they finally gave me what i wanted.