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JEE Main & Advanced Mathematics Relations Question Bank Mock Test - Relations and Functions

  • question_answer
    Let \[g(x)=f(x)-1.\] If \[f(x)+f(1-x)=2\forall x\in R\], then \[g(x)\] is symmetrical about

    A) the origin          

    B) the line\[x=\frac{1}{2}\]

    C) the point (1, 0)

    D) the point \[\left( \frac{1}{2},0 \right)\]

    Correct Answer: D

    Solution :

    [d] \[f(x)-1+f(1-x)-1=0\] So, \[g(x)+g(1-x)=0.\] Replacing x by \[x+\frac{1}{2}\], we get \[g\left( \frac{1}{2}+x \right)+g\left( \frac{1}{2}-x \right)=0.\] So, it is symmetrical about \[\left( \frac{1}{2},0 \right)\]


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