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If the real-valued function is \(f(x)=\dfrac{\sqrt{4-x^2}}{x-1}\), which of the following is its domain?यदि वास्तविक-मान फलन \(f(x)=\dfrac{\sqrt{4-x^2}}{x-1}\) है, तो इसका प्रांत (domain) कौन-सा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \([-2,1)\cup(1,2]\)\([-2,1)\cup(1,2]\)
For the square root, \(4-x^2\ge0\), so \(-2\le x\le2\). But the denominator cannot be zero, hence \(x=1\) is excluded. Exam tip: apply radical and denominator restrictions together.वर्गमूल परिभाषित होने के लिए \(4-x^2\ge0\), अतः \(-2\le x\le2\)। लेकिन हर \(x-1\) शून्य नहीं हो सकता, इसलिए \(x=1\) हटेगा। परीक्षा टिप: वर्गमूल और हर, दोनों की शर्तें साथ लगाएँ।
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