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If (f:\mathbb{R}\to\mathbb{R}), (f(x)=\lfloor x\rfloor), is (f) onto or not?यदि (f:\mathbb{R}\to\mathbb{R}), (f(x)=\lfloor x\rfloor) है, तो (f) आच्छादी है या नहीं?
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Correct answer:सही उत्तर: It is not ontoयह आच्छादी नहीं है
Step 1: (\lfloor x\rfloor) always gives an integer value. Step 2: The codomain (\mathbb{R}) contains non-integer real values such as (\frac{1}{2}), which are not obtained. Step 3: An integer-valued function is not onto (\mathbb{R}).चरण 1: (\lfloor x\rfloor) हमेशा पूर्णांक मान देता है। चरण 2: सहप्रांत (\mathbb{R}) में (\frac{1}{2}) जैसे अपरिमेय नहीं, बल्कि गैर-पूर्णांक वास्तविक मान भी हैं, जो नहीं मिलते। चरण 3: पूर्णांक-मान फलन (\mathbb{R}) पर आच्छादी नहीं होता।
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