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If (f:\mathbb{R}\to\mathbb{R}), (f(x)=\lfloor x+2\rfloor), why is (f) not onto?यदि (f:\mathbb{R}\to\mathbb{R}), (f(x)=\lfloor x+2\rfloor) है, तो (f) आच्छादी क्यों नहीं है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Because non-integer real values are not obtainedक्योंकि गैर-पूर्णांक वास्तविक मान नहीं मिलते
Step 1: (\lfloor x+2\rfloor) is always an integer. Step 2: The codomain (\mathbb{R}) contains non-integer values such as (\frac{1}{3}), which are not in the range. Step 3: An integer-valued function is not onto the whole real codomain.चरण 1: (\lfloor x+2\rfloor) हमेशा पूर्णांक होता है। चरण 2: सहप्रांत (\mathbb{R}) में (\frac{1}{3}) जैसे गैर-पूर्णांक मान हैं, जो परास में नहीं आते। चरण 3: पूर्णांक-मान फलन पूरे वास्तविक सहप्रांत पर आच्छादी नहीं होता।
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