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KVPY Sample Paper KVPY Stream-SX Model Paper-24

  • question_answer
    If \[f(x)={{\left( [\{x\}]{{\tan }^{-1}}\left( \frac{{{x}^{2}}-3x-1}{{{x}^{2}}-3x+5} \right)+3-{{x}^{7}} \right)}^{1/7}},\]where \[[k]\] and \[\{k\}\]denotes greatest integer and fractional part functions of k respectively, then the value of  \[{{f}^{-1}}(50)+f\,(f\,(100))-f\,(50),\]

    A) 0

    B) 25

    C) 50        

    D) 100

    Correct Answer: D

    Solution :

    \[f(x)={{(3-{{x}^{7}})}^{1/7}}\]
    \[f(f(x))={{(3-{{(f(x))}^{7}})}^{1/7}}={{[3-{{({{(3-{{x}^{7}})}^{1/7}})}^{7}}]}^{1/7}}=x\]
    \[{{f}^{-1}}(x)=f(x)\]
    \[\therefore {{f}^{-\,1}}(50)=f(50)\,\,\,and\,\,\,f(f(100))=100\]


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