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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2013

  • question_answer
        If\[f(x)\]satisfies the relation\[f\left( \frac{3x-y}{2} \right)=\frac{3f(x)-f(y)}{2},\forall x,y\in R,f(0)=2\]and\[f(0)=1,\]then the value of\[f(2)\]is

    A)  3

    B)  \[-4\]

    C)  5

    D)  None of the above

    Correct Answer: D

    Solution :

                    Given, \[f\left( \frac{3x-y}{2} \right)=\frac{3f(x)-f(y)}{2}\] \[\Rightarrow \]               \[f\left( \frac{3x-y}{3-1} \right)=\frac{3f(x)-f(y)}{3-1}\]which satisfies section formula for abscissa on LHS and ordinate on RHS. Hence,\[f(x)\]must be the linear function (as only straight line satisfies such section formula). Hence,     \[f(x)=ax+b\] But        \[f(0)=2\Rightarrow b=2,r(0)=1\] \[\Rightarrow \]               \[a=1\] Thus,       \[f(x)=x+2\] \[\therefore \]  \[f(2)=4\]


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