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RAJASTHAN ­ PET Rajasthan PET Solved Paper-2009

  • question_answer
    If \[f:R\to R\] is defined as \[f(x)={{(1-x)}^{1/3}}\] then \[{{f}^{-1}}(x)\] is

    A)   \[{{(1-x)}^{-1/3}}\]

    B)   \[{{(1-x)}^{3}}\]

    C)   \[1-{{x}^{3}}\]

    D)   \[1-{{x}^{1/3}}\]

    Correct Answer: C

    Solution :

     Given, \[f(x)=y={{(1-x)}^{1/3}}\] \[\Rightarrow\] \[{{y}^{3}}=1-x\] \[\Rightarrow\] \[x=1-{{y}^{3}}\] \[\therefore\] \[{{f}^{-1}}(x)=1-{{x}^{3}}\]


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