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U.S. regulators are investigating whether beleaguered crypto-exchange FTX.com mishandled customer funds, and they're looking into the firm's relationships with other parts of Sam Bankman-Fried's crypto empire.

The inquiries by the Securities and Exchange Commission and the Commodity Futures Trading Commission relate to the liquidity crisis that has pushed FTX to the brink, according to three people familiar with the matter. The SEC's scrutiny started months ago as a probe into FTX US and its crypto-lending activities, said two of the people, who who weren't authorized to speak publicly on the matter.

FTX's turmoil led to a tentative rescue offer by rival exchange Binance Holdings Ltd., which on Wednesday backed off of the offer. Binance founder Changpeng "CZ" Zhao walked away from his bailout almost as quickly as he offered a rescue.

"Our hope was to be able to support FTX's customers to provide liquidity, but the issues are beyond our control or ability to help," Binance said in a statement.

American regulators are also looking into the platform's relationship with its American counterpart FTX US and Bankman-Fried's trading house Alameda Research, two of the people said.

Representatives for the SEC and Binance declined to comment. The CFTC, FTX and FTX US didn't immediately respond to requests for comment.

The troubles at FTX.com follow high-profile collapses this year by crypto firms that have prompted calls for more U.S. regulation. Although various Washington agencies claim some turf, questions over who should oversee trading platforms continue to swirl.

The CFTC's jurisdiction over crypto is generally limited to derivatives, but the agency can take enforcement action if it believes there's fraud or manipulation in the underlying market. The SEC claims oversight over digital coins that qualify as securities under its rules. Both regulators also oversee investment firms.

In recent days, the regulators have asked for details about the ownership structure of FTX US and FTX.com, which caters to non-American clients, according to two of the people. Regulators are interested in any overlap between management and board structures, and the financial relationship between the two entities. The agencies have also asked for details on whether customer accounts were properly segregated and the composition of the investor base at FTX.com, said one of the people.

SEC Chair Gary Gensler has repeatedly warned about risks associated with digital-asset exchanges. He has said that many platforms may be violating securities laws by offering unregistered securities to Americans, improperly providing loans, or even front-running their clients' trades. Gensler has also raised concerns that firms may be engaged in conflicting lines of business and suggested that they should potentially split up the different functions.

Top CFTC officials have expressed concerns about the risk of crypto platforms mishandling customer assets. "There is not enough awareness or attention on this critical area where customer protections dovetail with financial stability risks," Democratic CFTC Commissioner Christy Goldsmith Romero said in a speech last month without mentioning any firms by name.

Bitcoin, the largest token by market value, fell as much as 9.9% to $16,853 on Wednesday. That brings this week's decline to almost 20%.