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What is the domain of \(f(x)=\frac{1}{\sqrt{x-1}}\)?\(f(x)=\frac{1}{\sqrt{x-1}}\) का domain क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \((1,\infty)\)\((1,\infty)\)
For \(\frac{1}{\sqrt{x-1}}\), the expression \(\sqrt{x-1}\) must be defined and also cannot be \(0\) because it is in the denominator.
So we need \(x-1>0\Rightarrow x>1\). Therefore the domain is \((1,\infty)\).\(\frac{1}{\sqrt{x-1}}\) में \(\sqrt{x-1}\) का defined होना आवश्यक है और यह denominator में होने के कारण \(0\) नहीं हो सकता।
अतः \(x-1>0\Rightarrow x>1\)। इसलिए domain \((1,\infty)\) है।
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