NCERT · Class 11 · Mathematics · Relations and FunctionsThe domain of the real function $f(x) = \frac{1}{\sqrt{x^2 - 4}}$ is:
Step-by-Step Solution
For $f(x)$ to be defined, the expression inside the square root must be strictly greater than zero: $x^2 - 4 > 0 \implies x^2 > 4 \implies |x| > 2$. This means $x < -2$ or $x > 2$, which can be written in interval notation as $(-\infty, -2) \cup (2, \infty)$. Thus, option C is correct.
Detailed Options Breakdown
Option : [-2, 2]
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Relations and Functions.
Option 1: (-2, 2)
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Relations and Functions.
Option 2: (-∞, -2) ∪ (2, ∞) (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 3: (-∞, -2] ∪ [2, ∞)
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Relations and Functions.
💡 Study Guide: This question tests core syllabus concepts from Relations and Functions. For formulas, key summaries, and mock exam reference guides, read the full Relations and Functions Revision Notes.