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Which of the following functions has the set of all real numbers as its domain?निम्नलिखित में से किस फलन का प्रांत सभी वास्तविक संख्याओं का समुच्चय है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(f(x)=x^2+1\)\(f(x)=x^2+1\)
The polynomial \(x^2+1\) is defined for every real \(x\), so its domain is \(\mathbb{R}\). In \(\frac{1}{x-3}\), \(x=3\) is excluded. Exam tip: first check denominator and square-root restrictions.बहुपद फलन \(x^2+1\) प्रत्येक वास्तविक \(x\) के लिए परिभाषित है, इसलिए इसका प्रांत \(\mathbb{R}\) है। \(\frac{1}{x-3}\) में \(x=3\) वर्जित है। परीक्षा टिप: हर और वर्गमूल की शर्त पहले जाँचें।
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