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If (f:\mathbb{R}\to\mathbb{R}), (f(x)=x^6+x^2+1), why is (f) not onto?यदि (f:\mathbb{R}\to\mathbb{R}), (f(x)=x^6+x^2+1), तो (f) सर्वाच्छादक क्यों नहीं है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Because (0) is not obtainedक्योंकि (0) नहीं मिलता
Step 1: Since (x^6\ge0) and (x^2\ge0), (x^6+x^2+1\ge1). Step 2: The codomain (\mathbb{R}) contains (0), but it cannot be in the range. Step 3: Once a lower bound is found, look for codomain values below it.चरण 1: (x^6\ge0) और (x^2\ge0), इसलिए (x^6+x^2+1\ge1)। चरण 2: सहप्रांत (\mathbb{R}) में (0) है, पर वह परास में नहीं आ सकता। चरण 3: निचली सीमा मिलते ही उससे छोटे सहप्रांत मान खोजें।
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