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What is the domain of the real-valued function \(f(x)=\frac{1}{x}\)?वास्तविक मान वाली फलन \(f(x)=\frac{1}{x}\) का डोमेन क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(\{x\in\mathbb{R}\mid x\ne 0\}\)\(\{x\in\mathbb{R}\mid x\ne 0\}\)
For \(f(x)=\frac{1}{x}\) to be defined, the denominator cannot be zero. So \(x\ne 0\). Therefore the domain is \(\{x\in\mathbb{R}\mid x\ne 0\}=( -\infty,0)\cup(0,\infty)\).\(f(x)=\frac{1}{x}\) परिभाषित होने के लिए हर (denominator) शून्य नहीं होना चाहिए। इसलिए \(x\ne 0\)। अतः डोमेन \(\{x\in\mathbb{R}\mid x\ne 0\}=( -\infty,0)\cup(0,\infty)\) है।
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