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If (f:\mathbb{R}\to\mathbb{R}), (f(x)=\sin x), why is (f) not one-one?यदि (f:\mathbb{R}\to\mathbb{R}), (f(x)=\sin x), तो (f) एकैकी क्यों नहीं है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Because (f(0)=f(\pi))क्योंकि (f(0)=f(\pi))
Step 1: Trigonometric functions are periodic. Step 2: (\sin 0=0) and (\sin \pi=0), while (0\ne \pi). Step 3: Periodic functions are generally not one-one on the entire real domain.चरण 1: त्रिकोणमितीय फलन आवर्ती होते हैं। चरण 2: (\sin 0=0) और (\sin \pi=0), जबकि (0\ne \pi)। चरण 3: आवर्ती फलन को पूरे वास्तविक क्षेत्र पर सामान्यतः एकैकी नहीं माना जाता।
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