Maths · Functions

The domain of =\log _{\mathbf{x}}\left(\mathbf{9}-\mathbf{x}^{2}\right) \) is

The domain of \( \mathbf{f}(\mathbf{x})=\log _{\mathbf{x}}\left(\mathbf{9}-\mathbf{x}^{2}\right) \) is

  • A. (-3,3)
  • B. \( (0, \infty) \)
  • C. (0,1)\( \cup(1, \infty) \)
  • D. (0,1)\( \cup(1,3) \)

Step-by-step solution

The base x must be positive and not equal to 1: x > 0, x ≠ 1. The argument 9 - x^2 must be positive: 9 - x^2 > 0 ⇒ x^2 < 9 ⇒ -3 < x < 3. Intersecting these conditions gives x ∈ (0,1) ∪ (1,3).
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