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Which of the following real-valued functions has the set of all real numbers as its domain?निम्नलिखित में से किस वास्तविक-मूल्य फलन का प्रांत (domain) सभी वास्तविक संख्याओं का समुच्चय है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(f(x)=x^2-3x+1\)\(f(x)=x^2-3x+1\)
The polynomial \(x^2-3x+1\) is defined for every real \(x\), so its domain is \(\mathbb{R}\). In contrast, \(\sqrt{x-1}\) requires \(x\ge1\). Exam tip: first check restrictions from roots, denominators and logs.बहुपद \(x^2-3x+1\) हर वास्तविक \(x\) के लिए परिभाषित है, इसलिए इसका प्रांत \(\mathbb{R}\) है। \(\sqrt{x-1}\) में \(x\ge1\) चाहिए। परीक्षा टिप: मूल, हर और लॉग की शर्तें पहले जाँचें।
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