Question:
The domain of the real valued function
\[
f(x) = \frac{x + 2}{9 - x^2}
\]
is
The domain of the real valued function
\[
f(x) = \frac{x + 2}{9 - x^2}
\]
is
Show Hint
For rational functions, always exclude values that make the denominator zero.
Updated On: Mar 28, 2026
- \( -3 \le x \le 3 \)
- \( \mathbb{R} \setminus \{-3, 3\} \)
- \( \mathbb{R} \)
- \( \mathbb{R} \setminus \{3\} \)
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The Correct Option is B
Solution and Explanation
Step 1: Identify the denominator.
The function is undefined when the denominator is zero.
Step 2: Solve for restricted values.
\[ 9 - x^2 = 0 \Rightarrow x^2 = 9 \Rightarrow x = \pm 3 \]
Step 3: Write the domain.
All real numbers except \(x = -3\) and \(x = 3\).
The function is undefined when the denominator is zero.
Step 2: Solve for restricted values.
\[ 9 - x^2 = 0 \Rightarrow x^2 = 9 \Rightarrow x = \pm 3 \]
Step 3: Write the domain.
All real numbers except \(x = -3\) and \(x = 3\).
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