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J & K CET Engineering J and K - CET Engineering Solved Paper-2007

  • question_answer
    If \[f:R\to R\] is given by \[f(x)=\left\{ \begin{matrix}    -1,\,when\,\,x\,\,is\,\,rational  \\    1,\,when\,\,x\,\,is\,\,irrational  \\ \end{matrix} \right.\] then \[(fof)\,(1-\sqrt{3})\] is equal to

    A)  \[1\]             

    B)  \[-1\]

    C)  \[\sqrt{3}\]           

    D)  \[0\]

    Correct Answer: B

    Solution :

    Given,  \[f(x)=\left\{ \begin{matrix}    -1,\,where\,\,x\,\,is\,rational  \\    1,\,when\,\,x\,is\,\,irrational\,  \\ \end{matrix} \right.\] Now, \[(fof)\,(1-\sqrt{3})=f[f(1-\sqrt{3})]=f(1)=-1\]


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