In recent years, the private equity industry has escaped much of the regulatory scrutiny that has been directed toward hedge funds and Wall Street banks. But that appears to be changing. The Securities and Exchange Commission has begun a broad examination of the private equity industry, seeking information about the business practices of some of the country’s most powerful financial firms. The SEC’s enforcement unit sent a letter late last year to several private equity funds as part of what it called an “informal inquiry’’ into the industry, according to two people with direct knowledge of the matter who requested anonymity because they were not authorized to discuss it publicly. It is not clear which firms received the letter.