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If \(f:\mathbb{R}\to\mathbb{R}\), \(f(x)=x^2+x+1\), why is (f) not onto?यदि \(f:\mathbb{R}\to\mathbb{R}\), \(f(x)=x^2+x+1\), तो (f) आच्छादक क्यों नहीं है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Because \(f(x)\ge\frac{3}{4}\), so many real values are missedक्योंकि \(f(x)\ge\frac{3}{4}\), इसलिए कई वास्तविक मान छूटते हैं
Step 1: \(x^2+x+1=\left(x+\frac{1}{2}\right)^2+\frac{3}{4}\). Step 2: Its minimum value is \(\frac{3}{4}\), so real values below it are missed. Step 3: Completing the square is a useful way to find the range.चरण 1: \(x^2+x+1=\left(x+\frac{1}{2}\right)^2+\frac{3}{4}\)। चरण 2: इसका न्यूनतम मान \(\frac{3}{4}\) है, अतः उससे छोटे वास्तविक मान नहीं मिलते। चरण 3: वर्ग पूरा करके परास निकालना बहुत उपयोगी तरीका है।
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