The cost of hospital care in Fairfax County will increase 7.5 per cent next year if hospital trustees approve a budget released yesterday by the Fairfax Hospital Association. The proposed increase is more than three times greater than this year's 2 percent rise.

Although the association, which operates Fairfax, Commonwealth Doctors and Mount Vernon Hospitals, said it was proposing a "bare-bones budget," Fairfax County Executive Leonard Whorton, in a report to the Board of Supervisors, called some proposed increases "alarming."

Futhermore, the county health care advisory board, which counsels the supervisors, has complained "that what information is available in the budget does not indicate that a serious effort at cost containment was made."

Neither the health care advisory board, Whorton, or the Board of Supervisors has the power of veto any part of the budget. The most they can do is exert pressure on the hospital association's trustees - who make the final decision - to hold down expenses.

The rate for semi-private rooms would go from $95 to $99 daily and the rate for private rooms would go from $112 to $116, under the trustees' proposal. The cost of a semi-private room in the metropolitan area ranges from $75 a day at Sqburban Hospital in Bethesda to $195.21 at D.C. General in Washington. Private rooms cost from $15 to $30 more.

There would be proportionately bigger increases for special care and other services. For example, daily cost for intensive coronary care would rise from $243 to $282, routine pediatric care, from $106 to 131 and regular nursery care, from $57 to 68.

There would be a 22 per cent increase for anesthesia, 20 per cent increase for operating room use and a 21 per cent increase for operating room use and a 21 per cent increase in the basic walk-in emergency fee.

The hospital association, in defending its budget, said ". . . we are able to hold our forecasted increase to this relatively low percentage (7.5 per cent) because of the association's aggressive, system-wide cost containment effort."

But neither County Executive Whorton nor the health care advisory board was convinced that costs were adequately contained.

The cost of hospital care has been escalating both locally and nationally, and the Carter administration has proposed a lid of about 9 per cent on further annual increases.

Whorton's memo to the supervisors, prepared by his health-care expert, Linda Shelton, said that because of rate increase and the wider range of services, average daily charges for a patient will average $223.22 at Fairfax Hospital, an increase of 12.7 per cent. The increase at Commonwealth would be 6.8 per cent and at Mount Vernon, 7.3 per cent, according to Whorton's memo.

The hospital association's budget forecasts that Mount Vernon Hospital, which opened last year amid criticism that it was unnecessary, will have 120 of its 235 beds in operation in 1978 - fewer than projected last year. At present, only 98 beds are in service.

The hospital association trustees will consider the budget Wednesday. The Board of Supervisors, armed with Whorton's memo and the one from the health care advisory board, will take up the issue two days earlier.