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  3. CEE Kerala Engineering

CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2003

  • question_answer
    If \[f(x)=\frac{1-x}{1+x}(x\ne -1),\]then\[{{f}^{-1}}(x)\]W equals to:

    A)  \[f(x)\]

    B)         \[\frac{1}{f(x)}\]             

    C)         \[-f(x)\]              

    D)         \[-\frac{1}{f(x)}\]

    E)  not defined

    Correct Answer: A

    Solution :

    Let \[y=f(x)=\frac{1-x}{1+x}\] \[\Rightarrow \]               \[y+yx=1-x\] \[\Rightarrow \]               \[1-y=x(1+y)\] \[\Rightarrow \]               \[x=\frac{1-y}{1+y}\] \[\therefore \]  \[{{f}^{-1}}(x)=\frac{1-x}{1+x}=f(x)\]


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