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If (f:\mathbb{R}\to\mathbb{R}), (f(x)=x^2-1), why is (f) not onto?यदि (f:\mathbb{R}\to\mathbb{R}), (f(x)=x^2-1), तो (f) आच्छादक क्यों नहीं है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Because (-2) is not an imageक्योंकि (-2) कोई प्रतिबिंब नहीं है
Step 1: Since (x^2\ge 0), we have (x^2-1\ge -1). Step 2: A value like (-2) is less than (-1), so it can never be attained. Step 3: To disprove onto property, one missing codomain element is enough.चरण 1: (x^2\ge 0), इसलिए (x^2-1\ge -1)। चरण 2: (-2) जैसा मान (-1) से छोटा है, इसलिए वह कभी नहीं मिल सकता। चरण 3: आच्छादक न होने के लिए सहप्रांत का एक छूटा हुआ अवयव दिखाना काफी है।
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