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JEE Main & Advanced Sample Paper JEE Main Sample Paper-36

  • question_answer
    If\[g=\{(1,\,\,1),\,\,(2,\,\,3),\,\,(3,\,\,5),\,\,(4,\,\,7)\}\] described by the formula, \[g(x)=\alpha \,\,x+\beta \] then what values should be assigned to \[\alpha \] and\[\beta ?\]

    A) \[\alpha =1,\,\,\beta =1\]                    

    B) \[\alpha =2,\,\,\beta =-1\]

    C) \[\alpha =1,\,\,\beta =-2\]      

    D) \[\alpha =-2,\,\,\beta =-1\]

    Correct Answer: B

    Solution :

     \[(1,\,\,1)\] satisfies\[g(x)=\alpha x+\beta \,\,\,\,\therefore \alpha +\beta =1\] \[(2,\,\,3)\] satisfies\[g(x)=\alpha x+\beta \,\,\,\,\therefore 2\alpha +\beta =3\] Solving the two equation, we get\[\alpha =2,\,\,\beta =-1\] It can be checked that other ordered pairs satisfy\[g(x)=2x-1\]


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