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JEE Main & Advanced Sample Paper JEE Main Sample Paper-44

  • question_answer
    If the graph of \[y=f(x)\] is symmetric about the curves \[x{{y}^{2}}-{{y}^{2}}+x-1=0\] and\[x{{y}^{2}}-3{{y}^{2}}+2x-6=0\], then fundamental period of \[f(x)\] is

    A)  4                                

    B)  3                 

    C)  2                                

    D)  1

    Correct Answer: A

    Solution :

     The given curve can be written as \[({{y}^{2}}+1)\,\,(x-1)=0\Rightarrow \,\,\,x=1\] \[({{y}^{2}}+2)\,(x-3)=0\,\Rightarrow \,\,x=3\] Hence, \[f(1+x)=f(1-x)\]         ?(i) \[f(3+x)=f(3-x)\]         ?(ii) From Eqs. (i) and (ii), we get \[f(x)=f(2-x)\] and      \[f(x)=f(6-x)\] \[\Rightarrow \]            \[f(2-x)=f(6-x)\] \[\Rightarrow \]            \[f(x+4)\]


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