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  3. CEE Kerala Engineering

CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2004

  • question_answer
    If\[f:R\to R\]is defined by\[f(x)={{x}^{2}}-6x-14,\] then\[{{f}^{-1}}(2)\]equals to:

    A)  {2, 8}                                    

    B)  \[\{-2,8\}\]

    C)  \[\{-2,-8\}\]        

    D)         \[\{2,-8\}\]

    E)  \[\{\phi \}\]

    Correct Answer: B

    Solution :

    Let \[y=f(x)={{x}^{2}}-6x-14\] \[\Rightarrow \]               \[{{x}^{2}}-6x-14=2\] \[\Rightarrow \]               \[{{x}^{2}}-6x-16=0\] \[\Rightarrow \]               \[{{x}^{2}}-8x+2x-16=0\] \[\Rightarrow \]               \[(x+2)(x-8)=0\] \[\Rightarrow \]        \[x=\{-2,8\}\]


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