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JCECE Engineering JCECE Engineering Solved Paper-2011

  • question_answer
    If\[f(x)=\frac{1-x}{1+x}\], the domain of\[{{f}^{-1}}(x)\]is

    A) \[R\]                                     

    B) \[R-\{-1\}\]

    C) \[(-\infty ,\,\,-1)\]                          

    D) \[(-1,\,\,\infty )\]

    Correct Answer: B

    Solution :

    Let\[f(x)=y\], then\[\frac{1-x}{1+x}=y\] \[\Rightarrow \]               \[x=\frac{1-x}{1+y}\] Thus,     \[{{f}^{-1}}(y)=\frac{1-x}{1+x}\] Clearly,\[{{f}^{-1}}(x)\] is denned for\[1+x\ne 0\]. Hence, domain of\[{{f}^{-1}}(x)\]is\[R-\{1\}\].


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