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What is the range of the function \(f(x)=\cos x\) when \(x\in[0,\pi]\)?फलन \(f(x)=\cos x\) का परिसर (range) क्या है, जब \(x\in[0,\pi]\)?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \([-1,1]\)\([-1,1]\)
On the interval \([0,\pi]\), \(\cos x\) decreases continuously from \(\cos 0=1\) to \(\cos\pi=-1\). Since both endpoints are included, every value from \(-1\) to \(1\) is attained, so the range is \([-1,1]\). Exam tip: for cosine over \([0,\pi]\), check the endpoint values first; they give the complete range.अंतराल \([0,\pi]\) में \(\cos x\) लगातार घटता है: \(\cos 0=1\) और \(\cos\pi=-1\)। इसलिए इस अंतराल में \(\cos x\) के सभी मान \(-1\) से \(1\) के बीच आते हैं और दोनों सिरों के मान शामिल हैं; अतः परिसर \([-1,1]\) है। परीक्षा में \([0,\pi]\) पर cosine का मान-परास याद रखें: \([-1,1]\)।
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