JEE Main & Advanced Mathematics Functions Question Bank Functions

  • question_answer
    If \[f(x)={{(a-{{x}^{n}})}^{1/n}},\]where \[a>0\]and n is a positive integer, then \[f[f(x)]=\]         [IIT 1983; UPSEAT 2001, 04]

    A)            \[{{x}^{3}}\]

    B)            \[{{x}^{2}}\]

    C)            \[x\]

    D)            None of these

    Correct Answer: C

    Solution :

               \[f[f(x)]={{[a-{{\left\{ f(x) \right\}}^{n}}]}^{1/n}}={{[a-(a-{{x}^{n}})]}^{1/n}}=x\].


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