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J & K CET Engineering J and K - CET Engineering Solved Paper-2012

  • question_answer
    Let R be the set of real numbers and \[f:R\to R\] be a function defined by \[f(x)={{x}^{2}}+4.\] Then, \[{{f}^{-1}}(29)\]equals to

    A)  \[\phi \]

    B)  \[\{5,\,\,\,-5\}\]

    C)  \[\{4,\,\,\,-4\}\]

    D)   \[\{2,\,\,\,-4\}\]

    Correct Answer: B

    Solution :

    Let \[y=f(x)={{x}^{2}}+4\] \[\Rightarrow \] \[{{x}^{2}}=y-4\] \[\Rightarrow \] \[x=\sqrt{y-4}\] \[\therefore \] \[{{f}^{-1}}(x)=\pm \sqrt{29-4}=\pm 5\]


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