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If (f:\mathbb{R}\to \mathbb{R}) is defined by (f(x)=x^2+4), is (f) onto?यदि (f:\mathbb{R}\to \mathbb{R}) को (f(x)=x^2+4) से परिभाषित किया गया है तो क्या (f) आच्छादक है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: No because numbers less than (4) are not obtainedनहीं क्योंकि (4) से छोटी संख्याएँ नहीं मिलतीं
Step 1: Since (x^2\ge 0), we have (x^2+4\ge 4). Step 2: The codomain is (\mathbb{R}), but the range is only ([4,\infty)). Step 3: Always compare the range with the codomain for onto questions.चरण 1: (x^2\ge 0) होता है इसलिए (x^2+4\ge 4)। चरण 2: सहक्षेत्र (\mathbb{R}) है पर परास केवल ([4,\infty)) है। चरण 3: आच्छादक जाँचते समय सहक्षेत्र और परास की बराबरी अवश्य देखें।
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