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The function (f:\mathbb{R}\to\mathbb{R}), (f(x)=x^2+4x+7), will be one-one on which set?फलन (f:\mathbb{R}\to\mathbb{R}), (f(x)=x^2+4x+7) किस समुच्चय पर एकैकी होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \([-2,\infty)\) / ([-2,\infty))\([-2,\infty)\) / ([-2,\infty))
Step 1: Write (f(x)=x^2+4x+7=(x+2)^2+3). Step 2: The vertex is at (x=-2), and the function is strictly increasing to the right of it. Step 3: A quadratic function is not one-one on all real numbers, but it is one-one on one side of its vertex.चरण 1: (f(x)=x^2+4x+7=(x+2)^2+3) लिखें। चरण 2: शीर्ष बिंदु (x=-2) है और इसके दाईं ओर फलन लगातार बढ़ता है। चरण 3: द्विघात फलन पूरे वास्तविक समुच्चय पर एकैकी नहीं होता, लेकिन शीर्ष के एक ओर एकैकी होता है।
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