JEE Main & Advanced Mathematics Functions Question Bank Self Evaluation Test - Relations and Functions-I

  • question_answer
    The domain and range of the relation R given by \[R=\{(x,y):y=x+\frac{6}{x};\}\] where \[x,y\in N\] and \[x<6\}\] is

    A) \[\{1,2,3\},\{7,5\}\]

    B)        \[\{1,2\},\{7,5\}\]

    C) \[\{2,3\},\{5\}\]

    D)                    None of these

    Correct Answer: A

    Solution :

    [a] When \[x=1,y=7\in N,\,\,so\,\,(1,7)\in R\] when \[x=2,y=2+3=5\in N,so(2,5)\in R\] Again for \[x=3,y=3+2=5\in N,(3,5)\in R\] similarly for \[x=4,y=4+\frac{6}{4}\notin N\] and for x = 5, \[y=5+\frac{6}{5}\notin N.\] Thus, \[R=\{(1,7),(2,5),(3,5)\}\] \[\therefore \] Domain of \[R=\{1,2,3\}\] and Range of \[R=\{7,5\}.\]


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