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If (f:[0,\pi]\to[-1,1]), where (f(x)=\cos x), which statement is correct about (f)?यदि (f:[0,\pi]\to[-1,1]) जहाँ (f(x)=\cos x), तो (f) के बारे में कौन सा कथन सही है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: It is both one-one and ontoयह एकैकी और आच्छादी दोनों है
Step 1: On ([0,\pi]), (\cos x) is strictly decreasing. Step 2: (\cos 0=1) and (\cos \pi=-1), so all values in ([-1,1]) occur. Step 3: A strictly monotonic function is one-one and becomes onto when its range equals the codomain.चरण 1: ([0,\pi]) पर (\cos x) लगातार घटता है। चरण 2: (\cos 0=1) और (\cos \pi=-1), इसलिए सभी मान ([-1,1]) में मिलते हैं। चरण 3: घटता या बढ़ता फलन एकैकी होता है और पूरा सहप्रांत ढकने पर आच्छादी भी।
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