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If (f:\mathbb{R}\to\mathbb{R}), (f(x)=ax^2+1), which statement is true?यदि (f:\mathbb{R}\to\mathbb{R}), (f(x)=ax^2+1), तो कौन सा कथन सत्य है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: It is not onto for any real (a)यह किसी भी वास्तविक (a) के लिए सर्वाच्छादक नहीं है
Step 1: If (a>0), the range is ([1,\infty)). Step 2: If (a<0), the range is ((-\infty,1]), and if (a=0), only (1) is obtained. Step 3: In no case is the range all of (\mathbb{R}), so it is not onto.चरण 1: यदि (a>0), तो परास ([1,\infty)) होगा। चरण 2: यदि (a<0), तो परास ((-\infty,1]) होगा और यदि (a=0), तो केवल (1) मिलेगा। चरण 3: किसी भी स्थिति में पूरा (\mathbb{R}) परास नहीं बनता, इसलिए सर्वाच्छादक नहीं है।
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