Find the domain of the rational function: g(x) = (2x + 1) / (x^2 - 9).
Answer and explanation
Correct answer: C. All real numbers except x = 3 and x = -3
- Step 1: A rational function is defined everywhere except where its denominator equals zero: x^2 - 9 = 0.
- Step 2: Solve for x: x^2 = 9 => x = 3 or x = -3.
- Step 3: Therefore, domain is all real numbers except x = 3 and x = -3.
Answer
All real numbers except x = 3 and x = -3.
Why not the others: Option 'All real numbers except x = 3' ignores the negative root x = -3. Option 'All real numbers except x = 9' sets the denominator without solving for x. Option 'All real numbers except x = -0.5' sets the numerator to zero.
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