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What is the correct answer about the one-one nature of (f:\mathbb{R}\to\mathbb{R}), (f(x)=x^5+x)?फलन (f:\mathbb{R}\to\mathbb{R}), (f(x)=x^5+x) की एकैकीता पर सही उत्तर क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: It is one-oneएकैकी है
Step 1: If (a>b), then (a^5>b^5) and (a>b). Step 2: Therefore (a^5+a>b^5+b), so the function is increasing. Step 3: An increasing function is one-one on its whole domain.चरण 1: (a>b) होने पर (a^5>b^5) और (a>b) होता है। चरण 2: इसलिए (a^5+a>b^5+b), अतः फलन बढ़ता है। चरण 3: बढ़ता हुआ फलन पूरे क्षेत्र पर एकैकी होता है।
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