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    Maths-
    General
    Easy

    Question

    text  If  end text f left parenthesis x right parenthesis equals open parentheses fraction numerator x over denominator 1 minus vertical line x vertical line end fraction close parentheses to the power of 1 divided by 2002 end exponent comma text  then  end text D subscript f text  is  end text

    1. R minus left square bracket negative 1 comma 1 right square bracket
    2. left parenthesis negative straight infinity comma A right parenthesis
    3. left parenthesis negative straight infinity comma negative 1 right parenthesis union left parenthesis 0 comma left parenthesis A right parenthesis
    4. None of these

    The correct answer is: left parenthesis negative straight infinity comma negative 1 right parenthesis union left parenthesis 0 comma left parenthesis A right parenthesis

      Let y equals fraction numerator x squared plus x plus 2 over denominator x squared plus x plus 1 end fraction
      not stretchy rightwards double arrow x squared left parenthesis y minus 1 right parenthesis plus x left parenthesis y minus 1 right parenthesis plus left parenthesis y minus 2 right parenthesis equals 0 comma straight for all x element of R
      Now, D greater or equal than 0 not stretchy rightwards double arrow left parenthesis y minus 1 right parenthesis squared minus 4 left parenthesis y minus 1 right parenthesis left parenthesis y minus 2 right parenthesis greater or equal than 0
      table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow left parenthesis y minus 1 right parenthesis left curly bracket left parenthesis y minus 1 right parenthesis minus 4 left parenthesis y minus 2 right parenthesis right curly bracket greater or equal than 0 end cell row cell not stretchy rightwards double arrow left parenthesis y minus 1 right parenthesis left parenthesis negative 3 y plus 7 right parenthesis greater or equal than 0 end cell end table

      not stretchy rightwards double arrow 1 less or equal than y less or equal than 7 over 3

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