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RAJASTHAN ­ PET Rajasthan PET Solved Paper-2004

  • question_answer
    Function is defined as\[f:x\to \frac{1+x}{1-x},\]then\[f\{f(x)\}\]is equal to

    A)  \[x\]                   

    B)  \[\frac{1}{x}\]

    C)  \[-x\]            

    D)  \[-\frac{1}{x}\]

    Correct Answer: D

    Solution :

     \[f[f(x)]=f\left[ \frac{1+x}{1-x} \right]\] \[=\frac{1+\frac{1+x}{1-x}}{1-\frac{1+x}{1-x}}\] \[=\frac{1-x+1+x}{1-x-1-x}=\frac{2}{-2x}=-\frac{1}{x}\]


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