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If the domain of the function is \(\mathbb{R}\), what is the range of \(f(x)=(x-2)^2+5\)?यदि फलन का प्रांत \(\mathbb{R}\) है, तो \(f(x)=(x-2)^2+5\) का परास क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \([5,\infty)\)\([5,\infty)\)
For every real \(x\), \((x-2)^2\ge 0\), so \(f(x)\ge 5\). Equality holds at \(x=2\), where \(f(2)=5\); therefore, 5 is included and the range is \([5,\infty)\).हर वास्तविक \(x\) के लिए \((x-2)^2\ge 0\), इसलिए \(f(x)\ge 5\)। \(x=2\) पर \(f(2)=5\), अतः 5 परास में शामिल है और परास \([5,\infty)\) है।
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