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JEE Main & Advanced Mathematics Functions Question Bank Functions

  • question_answer
    If \[f(x)=\frac{x-3}{x+1}\], then \[f[f\{f(x)\}]\] equals [RPET 1996]

    A)            x

    B)            ?x

    C)            \[\frac{x}{2}\]

    D)            \[-\frac{1}{x}\]

    Correct Answer: A

    Solution :

               \[f\,[f(x)]=\frac{f(x)-3}{f(x)+1}\]                    \[=\frac{\left( \frac{x-3}{x+1} \right)-3}{\left( \frac{x-3}{x+1} \right)+1}=\frac{x-3-3x-3}{x-3+x+1}=\frac{3+x}{1-x}\]            Now \[f\,[f(f(x))]=f\,\left( \frac{3+x}{1-x} \right)\]                                \[f(x)=(2,\,4]-\{3\}\].


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