Passengers who ride Metrobus routes that now serve Fairfax City will have an opportunity next week to praise or protest possible cutbacks in service.

Directors of the Metro Transit Authority will hold two hearings, in Washington on Tuesday and in Fairfax City on Wednesday, on a package of proposals growing out of the Fairfax City Council's recent decision to stop subsidizing Metrobus service. Fairfax City has estimated the cost of its subsidy next year at $280,000.

Metro must decide whether to halt all operations to the small suburban city, maintain faull service or initiate curtailed service - with Fairfax County paying the cost of operation.

Fairfax City has agreed to charter seven buses from Gray Line, a sightseeing bus company, to operate rush-hour commuter service to and from the Pentagon and downtown Washington.

The city plans to start the chartered service Tuesday. Metro has asked the Washington Metropolitan Area Transit Commissiion, a regulatory agency, to delay the adoption of Gray Line's tariff for the new service until at least Feb. 1. Metro says it wants to hold next week's public hearings and decide its own course of action.

If the commission turns down Metro's request, Fairfax City commuters will have their choice of Gray Line or Metrobus service until Metro reaches its final decision.

Metro's biggest problem in deciding future operations results from Fairfax City's geographic situation, rather like an island surrounded by Fairfax County, from which the city is politically independent.

Some Metorbus routes start west or south of Fairfax City and, because of the shape of the area's highway network, mush pass through the city on their way to Washington.

In general, Metor staff officials say the transit agency has three options: to leave the service as it is, to maintain existing service without stopping to pick up or discharge passengers in the city or to discontinue all ser ice in the city.

At present, Metro operates 64 eastbound and 67 westbound bus trips each weekday, picking up or discharging 992 passengers. Of the 992, an estimated 700 are residents of Fairfax City.

The two Metro hearings will be held at 7:30 p.m. Tuesday in Room 500 of the District Building, 14th and E Streets NW, Washington, and at 7:30 p.m. Wednesday in Fairfax City Hall, Armstrong Street, one block east of Rte. 123 (Ox Road). The follwoing summarizes the options to be considered on the eight affected Metrobus routes:

Route 3K, Lee Highway - (1) Maintain existing servicae. (2) Pick up and discharge passengers at George Mason University only. (3) Cuta back all service at Fairfax Circle.

Route 5K, Chain Bridge Road - (1) Mainntain existing service. (2) Pick up and discharge passengers at George Mason University only. (3) Cut back all service at Oakton.

Route 20E, Fairfax Express - (1) Maintain existing service. (2) Pick up and discharge passengers at George Mason University only. (3) Cut back all service at Blake Lane.

Route 20F, Arlington Boulevard - (1) Maintain existing operation. (2) Cut back all service at Fairfax Circle.

Routes 20K and 20M, Arlington Boulevard - (1) Maintain existing service. (2) Pick up and discharge passengers on Kamp Washington loop only. (3) Cut back all service at Fairfax Circle.

Route 29K, Alexandria-Fairfax - (1) Maintain existing service. (2) Pick up and discharge passengers at George Mason University only. (2) Reroute service around Fairfax City via Olley Lane and Braddock Road, terminating at the University.

Route 29Z, Greenbriar - (1) Maintain existing service. (2) Make stops inside the city only near the U.S. 50-U.S. 29-211 intersection, chiefly to serve county residents. (3) Discontinue all stops inside the city.