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∵a*b=ab+a+b,∴1*k=k+1+k=7,解得k=4或k=9,經檢驗知k=9不符合題意,∴k=4,∴f(x)=k*x=4x+4+x,∵x>0,∴f(x)的值域為:(4,+∞),故答案為:(4,+∞).
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