Question:
The domain of the function $f(x)=\sqrt{x^{2}+x-2}$ is:
The domain of the function $f(x)=\sqrt{x^{2}+x-2}$ is:
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Use the wavy curve method to solve quadratic inequalities.
Updated On: Apr 28, 2026
- $(-\infty,-2)\cup[1,\infty)$
- $(-\infty,-2]\cup(1,\infty)$
- $(-\infty,-2)\cup(1,\infty)$
- $(-\infty,-2]\cup[1,\infty)$
- $(-\infty,1)\cup[0,\infty)$
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The Correct Option is D
Solution and Explanation
Step 1: Concept
For the square root to be defined, the radicand must be non-negative: $x^2 + x - 2 \ge 0$.
Step 2: Factorization
$x^2 + 2x - x - 2 \ge 0 \implies (x + 2)(x - 1) \ge 0$.
Step 3: Interval Analysis
The roots are $-2$ and $1$. The inequality holds for $x \le -2$ or $x \ge 1$. Final Answer: (D)
For the square root to be defined, the radicand must be non-negative: $x^2 + x - 2 \ge 0$.
Step 2: Factorization
$x^2 + 2x - x - 2 \ge 0 \implies (x + 2)(x - 1) \ge 0$.
Step 3: Interval Analysis
The roots are $-2$ and $1$. The inequality holds for $x \le -2$ or $x \ge 1$. Final Answer: (D)
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