Question:
The domain of the function $f(x)=\sqrt{x^{2}+2x-15}$ is ________.
The domain of the function $f(x)=\sqrt{x^{2}+2x-15}$ is ________.
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Use the wavy curve method for quadratic inequalities.
Updated On: Jun 26, 2026
- $(-\infty,-5) \cup (3,\infty)$
- $(-\infty,-5) \cup [3,\infty)$
- $(-\infty,-5] \cup (3,\infty)$
- $(-\infty,-5] \cup [3,\infty)$
- $[-5,3]$
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The Correct Option is D
Solution and Explanation
Step 1: Concept
For a square root function, the expression inside must be $\ge 0$.
Step 2: Meaning
$x^{2}+2x-15 \ge 0 \implies (x+5)(x-3) \ge 0$.
Step 3: Analysis
The inequality holds when $x \le -5$ or $x \ge 3$.
Step 4: Conclusion
The domain is $(-\infty,-5] \cup [3,\infty)$. Final Answer: (D)
For a square root function, the expression inside must be $\ge 0$.
Step 2: Meaning
$x^{2}+2x-15 \ge 0 \implies (x+5)(x-3) \ge 0$.
Step 3: Analysis
The inequality holds when $x \le -5$ or $x \ge 3$.
Step 4: Conclusion
The domain is $(-\infty,-5] \cup [3,\infty)$. Final Answer: (D)
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