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The domain of the function f(x) = ⁻¹ ( ₂ ( x^2 + 2x + 5 x^2 + x + 2 ) ) is

Options

  1. A(- , -1] [1, )
  2. B(- , -3]
  3. C[-3, -1] [1, )
  4. DR

Correct answer

A. (- , -1] [1, )

Step-by-step solution

The given function is f(x) = ⁻¹ ( ₂ ( x^2 + 2x + 5 x^2 + x + 2 ) ) . For the domain of ⁻¹(y) , we must have -1 y 1 . Therefore, -1 ₂ ( x^2 + 2x + 5 x^2 + x + 2 ) 1 . This implies 2⁻¹ x^2 + 2x + 5 x^2 + x + 2 2^1 , which gives 1 2 x^2 + 2x + 5 x^2 + x + 2 2 . Since the discriminant of x^2 + x + 2 is 1 - 8 = -7 0 for all real x . We can safely multiply the inequalities by x^2 + x + 2 . Case 1: Left inequality 1 2 (x^2 + x + 2) x^2 + 2x + 5 x^2 + x + 2 2x^2 + 4x + 10 x^2 + 3x + 8 0 The discriminant of this quadratic i

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