I invested in a company via SAFE note that has completely changed its business model since.

Can I ask for my investment back?

Yes. You can always ask for your investment back.

Do they have to give you your investment back?

That depends on what you agreed to in your contract. If it says you have a right to your money back if the business model changes, then you should get your money back. I suspect that isn't the case though.

There may be other avenues to get your money back as well - if the business model change was immediate, clearly premeditated, and done in an attempt to 'con' you into investing into something you didn't want to invest into, for example.

We obviously don't know the specifics so i doubt you'll hear a useful definitive answer here.

Probably not. (Although maybe yes if you invested a very small amount, in which case they might return it just to clean up their cap table and simplify future legals.) In general, investor power comes from:

1. Board control (fire and replace the founders)
2. Veto rights (prevent them from making certain major decisions)
3. Moral weight (they simply want to do what you want them to do)

As an early investor, you're unlikely to hold the board, and since the decision has already been made (or so it sounds like) that probably rules out vetos and moral weight.

If they've shifted to another scalable model, then the equity still holds value, and you can just ride it out for the long haul (even if you're not a huge fan of the change). If they're shifting to a non-scalable model without an option for an exit, then you can probably negotiate a shift to a dividend-based buyout (they pay you a share of profits over time, which gradually buys you out as an investor for some multiple of what you originally put in). I don't think they are legally obligated to do this, but most founders I know would, since you can cause a huge amount of problems for them by being a stubborn part of their cap table and by telling the story of what happened to potential future investors (note that if you torpedo their reputation like this then there's 0% chance of you getting anything back, so really only worth doing if they're truly bad seeds.)

The startup world is FULL of stories where companies didn't succeed until making a pivot to a completely unrelated project. Just because the product has "completely changed its business model" doesn't mean it is a bad investment or even that the founders lack vision. Listen to to the "How I Built This" podcast episode with Stewart Butterfield, the founder of Tumble AND Slack, both of which came off crazy pivots not really related to the original project. Stewart comments at one point in the episode how the investors really had no more to lose, so they just didn't ask for their investments back for the Slack pivot and it was "... the best financial decision of their lives".