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What is the correct statement about (f:[0,\pi]\to\mathbb{R}), (f(x)=\cos x)?फलन (f:[0,\pi]\to\mathbb{R}), (f(x)=\cos x) के बारे में सही कथन क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: It is one-oneएकैकी है
Step 1: On ([0,\pi]), (\cos x) is strictly decreasing. Step 2: A decreasing function is also one-one because two different inputs do not give the same image. Step 3: For one-one nature, increasing is not necessary; strictly decreasing is also enough.चरण 1: ([0,\pi]) पर (\cos x) लगातार घटता है। चरण 2: घटता हुआ फलन भी एकैकी होता है क्योंकि दो अलग आगत समान छवि नहीं देते। चरण 3: एकैकीता के लिए बढ़ना ही जरूरी नहीं, लगातार घटना भी पर्याप्त है।
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