Foundry Inspector

• WWizards of the Coast2016-09-20
  Official Ruling
  Once a player has announced an artifact spell, no player may take actions to try to remove Foundry Inspector from the battlefield before that spell's cost is locked in.
• WWizards of the Coast2016-09-20
  Official Ruling
  If an artifact spell has in its mana cost, choose the value for X first, and then reduce the cost by . For example, an artifact that costs with X chosen as 4 costs to cast if you control Foundry Inspector.

Rulings via Scryfall