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The function (f:\mathbb{R}\to\mathbb{R}), where (f(x)=-x^2), is not onto becauseफलन (f:\mathbb{R}\to\mathbb{R}) जहाँ (f(x)=-x^2), सर्वाच्छादक नहीं है क्योंकि
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (1) cannot be the image of any (x)(1) किसी भी (x) की छवि नहीं हो सकता
Step 1: (-x^2) is never positive. Step 2: The codomain (\mathbb{R}) contains (1), but no real (x) satisfies (-x^2=1). Step 3: Showing one missed codomain value is enough to prove not onto.चरण 1: (-x^2) कभी धनात्मक नहीं होता। चरण 2: सहप्रांत (\mathbb{R}) में (1) है पर कोई वास्तविक (x) ऐसा नहीं कि (-x^2=1)। चरण 3: सर्वाच्छादकता न होने के लिए एक छूटा मान दिखाना पर्याप्त है।
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