He asked me (whether - if) I had written my report or not.
Both are grammatically correct here.However, some people would prefer 'whether' because it is more formal than 'if'. 'Writing a report' is something formal. BTW, 'wether' can also be the only correct choice if you say "He asked me whether or not I had written my report." That's because 'if' can't be followed directly by or not.
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