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VIT Engineering VIT Engineering Solved Paper-2011

  • question_answer
    Let \[f:R\to R\]be defined as \[f(x)={{x}^{2}}+1,\] find \[{{f}^{-1}}(-5).\]

    A)  \[\{\,\phi \,\}\]

    B)  \[\phi \]

    C)  \[\{\,5\,\}\]

    D)  \[\{\,-5,\,\,5\,\}\]

    Correct Answer: B

    Solution :

    Let \[{{f}^{-1}}(-5)=x.\] Then, \[f(x)=-5\] \[\Rightarrow \]\[{{x}^{2}}+1=-\,5\] \[\Rightarrow \]\[{{x}^{2}}=-\,6\] \[\Rightarrow \]\[x=\pm \sqrt{-6}\] which does not belong to R. \[\therefore \]\[{{f}^{-1}}(-5)=\phi \]


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