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JEE Main & Advanced Sample Paper JEE Main Sample Paper-20

  • question_answer
    Let\[f:R\to R\]and\[{{f}_{n}}(x)=f({{f}_{n-1}}(x))\forall \]in\[\ge 2,\,\,n\in N\], the roots of equation\[{{f}_{3}}(x){{f}_{2}}(x)f(x)-25{{f}_{2}}(x)f(x)+175f(x)\]\[=375\]. Which also satisfy equation \[f(x)=x\] will be

    A) \[5\]                                     

    B) \[15\]

    C) \[10\]                                   

    D)  Both [a] and [b]

    Correct Answer: D

    Solution :

    \[{{f}_{2}}(x)=f(f(x))=f(x)=x\] \[{{f}_{3}}(x)=f({{f}_{2}}(x))=f(x)=x\] \[\Rightarrow \]\[{{x}^{3}}-25{{x}^{2}}+175x-375=0\] \[(x-5)({{x}^{2}}-20x+75)=0\] \[{{(x-5)}^{2}}(x-15)=0\Rightarrow x=5,\,\,15\]


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