J & K CET Engineering J and K - CET Engineering Solved Paper-2007

  • question_answer
    If the function \[f:R\to R\] denned by \[f(x)=[x]\]where \[[x]\] is the greatest integer not exceeding x, for \[x\in R\] then /is

    A)  even

    B)  odd

    C)  neither even nor odd

    D)  strictly increasing

    Correct Answer: C

    Solution :

    We know that, a function is said to be even, if \[f(-x)=f(x)\] and odd, if \[f(-x)=-f(x)\] and  \[f(x)\] is increasing, if \[f'(x)>0\] Here, \[f(x)\]is not differentiable at \[x\in I\] and above two cases are also not satisfied by \[f(x)\] \[\therefore \] \[f(x)=[x]\] is neither even nor odd.


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