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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2008

  • question_answer
    If \[f:R\to R\] is defined by \[f(x)={{x}^{3}},\] then \[{{f}^{-1}}(8)\]is equal to

    A)  \[\{2\}\]           

    B)  \[\{2,2\omega ,2{{\omega }^{2}}\}\]

    C)  \[\{2,-2\}\]

    D)  \[\{2,2\}\]

    Correct Answer: A

    Solution :

    Let    \[y=f(x)={{x}^{3}}\] \[\therefore \]  \[x={{y}^{1/3}}\] \[\Rightarrow \]               \[{{f}^{-1}}(x)={{x}^{1/3}}\] \[\Rightarrow \]               \[{{f}^{-1}}(8)={{(8)}^{1/3}}\]                 \[=2\]


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