The Fugitive Doctor

• WOTC Official Reminder Textofficial rules
  Investigate — Create a Clue token. It's an artifact with ", Sacrifice this artifact: Draw a card."

• WWizards of the Coast2023-10-13
  Official Ruling
  You must still follow any timing restrictions and permissions, including those based on the card's type. For instance, you can cast a sorcery using flashback only when you could normally cast a sorcery.
• WWizards of the Coast2023-10-13
  Official Ruling
  Neither "Time" nor "Lord" are creature types. Some older cards were printed with the subtype "Lord," but all of those cards have updated Oracle card text that removed that type.
• WWizards of the Coast2023-10-13
  Official Ruling
  If a card has multiple instances of flashback, you may choose any of its flashback costs to pay.
• WWizards of the Coast2023-10-13
  Official Ruling
  If an effect instructs you to choose a creature type, you may choose Time Lord.
• WWizards of the Coast2023-10-13
  Official Ruling
  If you cast an instant or sorcery with in its mana cost this way, you must choose 0 as the value of X. (You still have to pay .)
• WWizards of the Coast2023-10-13
  Official Ruling
  If a split card gains flashback, you pay only the cost of the half you're casting.
• WWizards of the Coast2023-10-13
  Official Ruling
  Unlike other creature types in Magic that are each only one word, the two words "Time Lord" represent a single creature subtype. Time Lord is the only two-word creature type.
• WWizards of the Coast2023-10-13
  Official Ruling
  "Investigate" means "Create a Clue token." A Clue token is a colorless Clue artifact token with ", Sacrifice this artifact: Draw a card."
• WWizards of the Coast2023-10-13
  Official Ruling
  To determine the total cost of a spell, start with the mana cost or alternative cost (such as a flashback cost) you're paying, add any cost increases, then apply any cost reductions. The mana value of the spell is determined only by its mana cost, no matter what the total cost to cast the spell was.
• WWizards of the Coast2023-10-13
  Official Ruling
  A spell cast using flashback will always be exiled afterward, whether it resolves, is countered, or leaves the stack in some other way.
• WWizards of the Coast2023-10-13
  Official Ruling
  "Flashback [cost]" means "You may cast this card from your graveyard by paying [cost] rather than paying its mana cost" and "If the flashback cost was paid, exile this card instead of putting it anywhere else any time it would leave the stack."

Rulings via Scryfall