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If (f:\mathbb{R}\to\mathbb{R}) and (f(x)=x^3+2x), which statement about (f) is correct?यदि (f:\mathbb{R}\to\mathbb{R}) तथा (f(x)=x^3+2x) हो तो (f) के बारे में सही कथन क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: It is one-oneयह एकैकी है
Step 1: (x^3+2x) is an increasing function. Step 2: If (a>b), then (a^3-b^3+2(a-b)>0), so (f(a)>f(b)). Step 3: A strictly increasing function is one-one.चरण 1: (x^3+2x) बढ़ने वाला फलन है। चरण 2: यदि (a>b) हो तो (a^3-b^3+2(a-b)>0), इसलिए (f(a)>f(b))। चरण 3: लगातार बढ़ता फलन एकैकी होता है।
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