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

  • question_answer
    If \[f(x)=\frac{\sin ([x]\pi )}{{{x}^{2}}+x+1}\] where [.] denotes the greatest integer function, then

    A) f is one-one

    B) f is not one-one and non-constant

    C) f is a constant function

    D) None of these

    Correct Answer: C

    Solution :

    [c] \[f(x)=\frac{\sin [x]\pi }{{{x}^{2}}+x+1}\]Let \[[x]=n\in \]integer \[\therefore \sin [x]\pi =0\] Or \[f(x)=0\] Hence, f(x) is constant function.


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