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Which of the following is the domain of the function \(f(x)=\frac{1}{\sqrt{x-2}}\)?फलन \(f(x)=\frac{1}{\sqrt{x-2}}\) का परिभाषा-क्षेत्र निम्नलिखित में से कौन-सा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(x>2\)\(x>2\)
The radicand \(x-2\) must be non-negative, but the denominator \(\sqrt{x-2}\) cannot be zero. Hence \(x-2>0\), so \(x>2\). Option B wrongly includes \(x=2\), where the denominator is zero. Exam tip: a square root in a denominator requires a strict inequality.वर्गमूल के भीतर \(x-2\) ऋणात्मक नहीं हो सकता और हर \(\sqrt{x-2}\) शून्य भी नहीं हो सकता। अतः \(x-2>0\), इसलिए \(x>2\)। विकल्प B में \(x=2\) शामिल है, जहाँ हर शून्य हो जाता है। परीक्षा टिप: हर वाले वर्गमूल के लिए असमता कठोर होती है।
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