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Question

Range of the function f left parenthesis x right parenthesis equals square root of fraction numerator x to the power of 2 end exponent minus 3 x minus 4 over denominator x to the power of 2 end exponent minus 3 x plus 4 end fraction end root is

  1. [0, 1]    
  2. [0, 1]    
  3. open square brackets negative fraction numerator 25 over denominator 7 end fraction comma 1 close parentheses    
  4. left parenthesis 0 comma infinity right parenthesis    

The correct answer is: [0, 1]


    Let y equals fraction numerator x to the power of 2 end exponent minus 3 x minus 4 over denominator x to the power of 2 end exponent minus 3 x plus 4 end fraction
    left parenthesis y minus 1 right parenthesis blank x to the power of 2 end exponent plus 3 left parenthesis y minus left parenthesis a right parenthesis blank x plus 4 left parenthesis y plus 1 right parenthesis blank equals 0
    Case-I If y = 1, then 8 = 0 (not possible)
    Case-II If y not equal to 1, then 9 left parenthesis y minus 1 right parenthesis to the power of 2 end exponent minus 16 left parenthesis y minus 1 right parenthesis blank left parenthesis y plus 1 right parenthesis blank greater or equal than 0
    i.e.blank left parenthesis y minus 1 right parenthesis blank left parenthesis 7 y plus 25 right parenthesis less or equal than 0
    i.e.blank minus fraction numerator 25 over denominator 7 end fraction less or equal than y less than 1
    Range of f(x) is [0, 1)

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