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The function (f:\mathbb{R}\to\mathbb{R}), where (f(x)=\lfloor x\rfloor), is not onto becauseफलन (f:\mathbb{R}\to\mathbb{R}) जहाँ (f(x)=\lfloor x\rfloor), सर्वाच्छादक नहीं है क्योंकि
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Real values like (\frac{1}{2}) are not images(\frac{1}{2}) जैसे वास्तविक मान छवि नहीं बनते
Step 1: (\lfloor x\rfloor) always gives an integer. Step 2: The codomain (\mathbb{R}) contains (\frac{1}{2}), but it is never an image. Step 3: The greatest integer function has range limited to integers.चरण 1: (\lfloor x\rfloor) हमेशा पूर्णांक देता है। चरण 2: सहप्रांत (\mathbb{R}) में (\frac{1}{2}) है, पर वह कभी छवि नहीं बनता। चरण 3: महत्तम पूर्णांक फलन में परास पूर्णांकों तक सीमित रहता है।
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