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Solution of the inequation log subscript 0.1 end subscript invisible function application open parentheses log subscript 2 end subscript invisible function application fraction numerator x to the power of 2 end exponent plus 1 over denominator vertical line x minus 1 vertical line end fraction close parentheses < 0 contains the interval

  1. (1, ∞)    
  2. (–∞, 1)    
  3. [1, ∞)    
  4. none of these    

The correct answer is: (1, ∞)


    l o g subscript 2 end subscript invisible function application open parentheses fraction numerator x to the power of 2 end exponent plus 1 over denominator vertical line x minus 1 vertical line end fraction close parentheses greater than 1 rightwards double arrow fraction numerator x to the power of 2 end exponent plus 1 over denominator vertical line x minus 1 vertical line end fraction greater than 2
    If x > 1 x2 + 1 > 2 |x – 1|
    x to the power of 2 end exponent plus 1 minus 2 x plus 2 greater than 0 for all x element of R
    If x less than 1 x to the power of 2 end exponent plus 1 greater than 2 minus 2 x
    x2 + 2x + 1 > 2
    rightwards double arrow x plus 1 greater than square root of 2 rightwards double arrow x greater than square root of 2 minus 1 alpha v delta x plus 1 less than negative square root of 2 rightwards double arrow x less than negative 1 minus square root of 2
    thus, x element of left parenthesis negative infinity comma negative 1 minus square root of 2 right parenthesis union left parenthesis square root of 2 minus 11 right parenthesis union left parenthesis 1 comma infinity right parenthesis

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