Sale of a mutual fund

My current broker sold a mutual fund that was purchased when I was with a different brokerage. I can't find the date that the shares were purchased originally. I know it is more than 10 years ago. How do I go about finding a cost basis?

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You can try online searches for historical prices for the company. However, if you don't know the date, you will just have to do the best you can.

You have to report the sale on your tax return. Lacking any cost basis, the IRS will consider the entire sale amount as taxable. So, you need to make your best effort to determine the original cost basis, even if (worst case) it's a guess. Historical prices of most mutual funds are readily available on the internet and should, at least, satisfy the IRS that your basis wasn't zero; just "google" fund name (or symbol) Historical Prices