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What is the domain of the function f(x) = √(x² − 1)?फलन f(x) = √(x² − 1) का प्रांत क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (−∞, −1] ∪ [1, ∞)(−∞, −1] ∪ [1, ∞)
The radicand must be non-negative: x² − 1 ≥ 0. Hence x² ≥ 1, so x ≤ −1 or x ≥ 1. Therefore, the domain is (−∞, −1] ∪ [1, ∞), including the endpoints where the radicand is zero.वर्गमूल का मूलांक गैर-ऋणात्मक होना चाहिए: x² − 1 ≥ 0। इसलिए x² ≥ 1, अर्थात x ≤ −1 या x ≥ 1। अतः प्रांत (−∞, −1] ∪ [1, ∞) है। सिरों पर मूलांक शून्य होने से वे शामिल हैं।
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