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If (f:\mathbb{Z}\to\mathbb{Z}), (f(n)=n^3), why is (f) not onto?यदि (f:\mathbb{Z}\to\mathbb{Z}), (f(n)=n^3) है, तो (f) आच्छादी क्यों नहीं है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Because an integer like (2) is not obtainedक्योंकि (2) जैसा पूर्णांक नहीं मिलता
Step 1: (n^3) is always a perfect cube. Step 2: The codomain (\mathbb{Z}) contains (2), but no integer (n) satisfies (n^3=2). Step 3: On an integer domain, a power function does not necessarily give all integers.चरण 1: (n^3) हमेशा पूर्ण घन होता है। चरण 2: सहप्रांत (\mathbb{Z}) में (2) है, लेकिन कोई पूर्णांक (n) ऐसा नहीं कि (n^3=2)। चरण 3: पूर्णांक प्रांत में घात फलन सभी पूर्णांक नहीं देता।
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