JEE Main & Advanced Mathematics Functions Question Bank Functions

  • question_answer
    If \[f(x)=\frac{x}{x-1}=\frac{1}{y}\], then \[f(y)=\] [MP PET 1995, 97]

    A)            x

    B)            \[x+1\]

    C)            \[x-1\]

    D)            \[1-x\]

    Correct Answer: D

    Solution :

               \[f(x)=\frac{x}{x-1}=\frac{1}{y}\,\,\Rightarrow \,\,\frac{-1}{x-1}=\frac{y-1}{y}\] {Applying dividendo}                    \[\Rightarrow \,\,\frac{x-1}{-1}=\frac{y}{y-1}\,\Rightarrow \,\,-x+1=f(y).\]


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