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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2006

  • question_answer
        If\[y=f(x)=\frac{x+2}{x-1},\]then

    A)  \[x=f(y)\]

    B)  \[f(1)=3\]

    C) \[y\]increases with\[x\]for\[x<1\]

    D) \[f\]is a rational function of\[x\]

    Correct Answer: A

    Solution :

                    Given, \[y=f(x)=\frac{x+2}{x-1}\] \[\therefore \]\[f(y)=f\left( \frac{x+2}{x-1} \right)=\frac{\frac{x+2}{x-1}+2}{\frac{x+2}{x-1}-1}\] \[f(y)=\frac{x+2+2x-2}{x+2-x+1}\] \[\Rightarrow \]               \[f(y)=\frac{3x}{3}=x\] \[\therefore \]  \[x=f(y)\]


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