JEE Main & Advanced Mathematics Functions Question Bank Functions

  • question_answer
    If \[f:[0,\ \infty )\to [0,\ \infty )\] and \[f(x)=\frac{x}{1+x},\]then f is            [IIT Screening 2003]

    A)            One-one and onto

    B)            One-one but not onto

    C)            Onto but not one-one

    D)            Neither one-one nor onto

    Correct Answer: B

    Solution :

               \[{f}'(x)=\frac{1}{{{(1+x)}^{2}}}>0,\,\forall x\in [0,\,\infty )\] and range \[\in [0,\,1)\]            Þ function is one-one but not onto.


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