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On which interval is (f:\mathbb{R}\to\mathbb{R}), (f(x)=x^2+x), one-one?फलन (f:\mathbb{R}\to\mathbb{R}), (f(x)=x^2+x) किस अंतराल पर एकैकी है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \([-\frac{1}{2},\infty)\) / ([-\frac{1}{2},\infty))\([-\frac{1}{2},\infty)\) / ([-\frac{1}{2},\infty))
Step 1: Write (x^2+x=(x+\frac{1}{2})^2-\frac{1}{4}). Step 2: The vertex is (x=-\frac{1}{2}), and the function increases to the right of it. Step 3: Completing the square quickly gives the one-one interval.चरण 1: (x^2+x=(x+\frac{1}{2})^2-\frac{1}{4}) लिखें। चरण 2: शीर्ष (x=-\frac{1}{2}) है और इसके दाईं ओर फलन बढ़ता है। चरण 3: पूर्ण वर्ग विधि से एकैकी अंतराल जल्दी मिल जाता है।
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