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Choose the correct statement about \(f:\mathbb{R}\to\left[\frac{3}{4},\infty\right)\), \(f(x)=x^2+x+1\).फलन \(f:\mathbb{R}\to\left[\frac{3}{4},\infty\right)\), \(f(x)=x^2+x+1\) के बारे में सही कथन चुनिए।
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: It is ontoयह आच्छादक है
Step 1: Completing the square gives \(f(x)=\left(x+\frac{1}{2}\right)^2+\frac{3}{4}\). Step 2: The range is \(\left[\frac{3}{4},\infty\right)\), the same as the codomain. Step 3: A function is onto when its range equals its codomain.चरण 1: वर्ग पूरा करने पर \(f(x)=\left(x+\frac{1}{2}\right)^2+\frac{3}{4}\)। चरण 2: परास \(\left[\frac{3}{4},\infty\right)\) है, जो सहप्रांत के समान है। चरण 3: सहप्रांत को परास के बराबर रखने पर फलन आच्छादक हो जाता है।
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