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JEE Main & Advanced Mathematics Functions Question Bank Self Evaluation Test - Relation and Functions-II

  • question_answer
    Let [x] denote the greatest integer \[\le x.\] If \[f(x)=[x]\] and \[g(x)=\left| x \right|,\]then the value of \[f\left( g\left( \frac{8}{5} \right) \right)-g\left( f\left( -\frac{8}{5} \right) \right)\]is

    A) 2

    B) -2

    C) 1

    D) -1

    Correct Answer: D

    Solution :

    [d] Given that, \[f(x)=[x]\]and \[g(x)=\left| x \right|\] Now, \[f\left( g\left( \frac{8}{5} \right) \right)=g\left( \frac{8}{5} \right)=\left[ \frac{8}{5} \right]=1\] And \[g\left( f\left( -\frac{8}{5} \right) \right)=g\left( \left[ -\frac{8}{5} \right] \right)=g(-2)=\left| -2 \right|=2\] \[\therefore f\left( g\left( \frac{8}{5} \right) \right)-g\left( f\left( -\frac{8}{5} \right) \right)=1-2=-1.\]


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