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For (f:\mathbb{R}\to[0,\infty)), where (f(x)=|x|), which statement is correct?फलन (f:\mathbb{R}\to[0,\infty)) जहाँ (f(x)=|x|), सही कथन कौन सा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (f) is onto but not one-one(f) सर्वाच्छादक है पर एकैकी नहीं
Step 1: For every (y\ge0), taking (x=y) gives (|x|=y). Step 2: But (|a|=|-a|), so different domain elements can have the same image. Step 3: Onto and one-one properties must be checked separately.चरण 1: हर (y\ge0) के लिए (x=y) लेने पर (|x|=y) मिलता है। चरण 2: लेकिन (|a|=|-a|), इसलिए अलग प्रांत अवयव एक ही छवि दे सकते हैं। चरण 3: सर्वाच्छादक और एकैकी गुण अलग-अलग जाँचना चाहिए।
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