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Is (f:\mathbb{R}\to\mathbb{R}), where (f(x)=\lfloor x\rfloor), onto or not?फलन (f:\mathbb{R}\to\mathbb{R}) जहाँ (f(x)=\lfloor x\rfloor), आच्छादी है या नहीं?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: No because only integer values are attainedनहीं क्योंकि केवल पूर्णांक मान मिलते हैं
Step 1: (\lfloor x\rfloor) is always an integer. Step 2: The codomain (\mathbb{R}) contains non-integers like (\frac{1}{2}), which are not attained. Step 3: Being defined everywhere and being onto are different ideas.चरण 1: (\lfloor x\rfloor) सदैव पूर्णांक होता है। चरण 2: सहप्रांत (\mathbb{R}) में (\frac{1}{2}) जैसे गैरपूर्णांक भी हैं, जो नहीं मिलते। चरण 3: परिभाषित होना और आच्छादी होना अलग बातें हैं।
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