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If (f:\mathbb{R}\to\mathbb{R}), (f(x)=\cos x), then (f) is not one-one. Which example is correct?यदि (f:\mathbb{R}\to\mathbb{R}), (f(x)=\cos x), तो (f) एकैकी नहीं है। कौन-सा उदाहरण सही है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (f(0)=f(2\pi))(f(0)=f(2\pi))
Step 1: (\cos x) is periodic. Step 2: (\cos 0=1) and (\cos 2\pi=1), while (0\ne 2\pi). Step 3: Periodicity on the whole real domain strongly proves the function is not one-one.चरण 1: (\cos x) आवर्ती फलन है। चरण 2: (\cos 0=1) और (\cos 2\pi=1), जबकि (0\ne 2\pi)। चरण 3: पूरे वास्तविक क्षेत्र पर आवर्तिता एकैकी न होने का मजबूत प्रमाण देती है।
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