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KVPY Sample Paper KVPY Stream-SX Model Paper-3

  • question_answer
     For \[x\in R-\{0,1\},\] let \[{{f}_{1}}(x)=\frac{1}{x},\]\[{{f}_{2}}(x)=1-x\] and \[{{f}_{3}}(x)=\frac{1}{1-x}\] be three-given functions. If a function, \[J(x)\] is equal to:

    A) \[{{f}_{3}}(x)\]

    B) \[{{f}_{1}}(x)\]

    C) \[{{f}_{2}}(x)\]                        

    D) \[\frac{1}{x}{{f}_{3}}(x)\]

    Correct Answer: A

    Solution :

    \[{{f}_{1}}(x)=\frac{1}{x},\] \[{{f}_{2}}(x)=1-x\], \[{{f}_{3}}(x)=\frac{1}{1-x}\]
    \[({{f}_{2}}ojo{{f}_{1}})(x)={{f}_{3}}(x)\]
    \[({{f}_{2}}oj)\left( \frac{1}{x} \right)=\frac{1}{1-x}\]
    \[{{f}_{2}}\left( J\left( \frac{1}{x} \right) \right)=\frac{1}{1-x}\]
    \[1-J\left( \frac{1}{x} \right)=\frac{1}{1-x}\]
    \[1-\frac{1}{1-x}=J\left( \frac{1}{x} \right)\]
    \[\Rightarrow \]   \[J\left( \frac{1}{x} \right)=\frac{1}{1-\frac{1}{x}}={{f}_{3}}(x).\]


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