BCECE Engineering BCECE Engineering Solved Paper-2008

  • question_answer If \[f:R\to R\]is defined by \[f(x)=[2x]-2[x]\] for all \[x\in R,\]where \[[x]\]is the greatest integer not exceeding x, then the range of\[f\]is

    A) \[\{x\in R:0\le x\le 1\}\]

    B)  \[(0,1)\]

    C)  \[\{x\in R:x>0\}\]

    D)  \[\{x\in R:x\le 0\}\]

    Correct Answer: B

    Solution :

    Given, \[f(x)=[2x]-2[x],\forall \,x\in R\] Let \[x\]is an integer, then \[f(x)=0\] and let \[x\]is not an integer, then \[f(x)=1\] \[\therefore \] Range of \[f(x)=\{0,1\}\]

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