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JEE Main & Advanced Sample Paper JEE Main Sample Paper-8

  • question_answer
    Let \[f:R\to R\]and \[{{f}_{n}}(x)=f({{f}_{n-1}}(x))\,\,\forall n\ge 2,\]\[n\in N.\]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 \[f(x)=-\text{ }x\]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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