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Why is the function (f:\mathbb{R}\to\mathbb{R}), where (f(x)=x^4+x^2), not onto?फलन (f:\mathbb{R}\to\mathbb{R}) जहाँ (f(x)=x^4+x^2), सर्वाच्छादक क्यों नहीं है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Because (-1) is not an imageक्योंकि (-1) छवि नहीं बनता
Step 1: Since (x^4\ge0) and (x^2\ge0), we have (x^4+x^2\ge0). Step 2: The codomain (\mathbb{R}) contains (-1), but no real (x) can map to it. Step 3: For sums of even powers, check negative codomain values first.चरण 1: (x^4\ge0) और (x^2\ge0), इसलिए (x^4+x^2\ge0)। चरण 2: सहप्रांत (\mathbb{R}) में (-1) है, पर कोई वास्तविक (x) इसे छवि नहीं बना सकता। चरण 3: सम घात वाले योग में ऋणात्मक सहप्रांत मान तुरंत जाँचें।
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