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KVPY Sample Paper KVPY Stream-SX Model Paper-29

  • question_answer
    Let \[N\] be the set of natural numbers and two functions\[f\] and \[g\] be defined as \[f,g:N\to N\] such that: \[f(n)=\left\{ \begin{matrix}    \frac{n+1}{2} & if\,n\,is\,odd  \\    \frac{n}{2} & if\,n\,is\,even  \\ \end{matrix} \right.\] and\[g(n)=n-{{(-1)}^{n}}.\]Then\[fog\]is:

    A) onto but not one-one.

    B) one-one but, not onto.

    C) both one-one and onto.

    D) neither one-one nor onto.

    Correct Answer: A

    Solution :

    \[\left. \begin{matrix}    f(g(1))=1  \\    f(g(2))=1  \\ \end{matrix} \right\}many\,one\]
    \[f(g(2k))=k\]
    \[f(g(2k+1))=k+1\]
    \[\therefore \] Onto


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