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If (f:\mathbb{R}\to\mathbb{Z}) and (f(x)=\lfloor x\rfloor), what is the correct statement about (f)?यदि (f:\mathbb{R}\to\mathbb{Z}) तथा (f(x)=\lfloor x\rfloor) है, तो (f) के लिए सही कथन क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (f) is not one-one(f) एक-एक नहीं है
Step 1: The greatest integer function maps many real numbers to the same integer. Step 2: For example (f(1.2)=1) and (f(1.8)=1), while (1.2\neq 1.8). Step 3: Step-like functions are generally not one-one.चरण 1: महत्तम पूर्णांक फलन कई वास्तविक संख्याओं को एक ही पूर्णांक देता है। चरण 2: जैसे (f(1.2)=1) और (f(1.8)=1), जबकि (1.2\neq 1.8)। चरण 3: सीढ़ी जैसे फलन सामान्यतः एक-एक नहीं होते।
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