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What is the domain of \(\cos^{-1}x\) for real \(x\)?वास्तविक \(x\) के लिए \(\cos^{-1}x\) का domain क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \([ -1, 1 ]\)\([ -1, 1 ]\)
Let \(y=\cos^{-1}x\). Then \(\cos y=x\). Since cosine has range \([-1,1]\), the input \(x\) must lie in \([-1,1]\). Therefore the domain of \(\cos^{-1}x\) is \([ -1,1 ]\).मान लीजिए \(y=\cos^{-1}x\). तब \(\cos y=x\). क्योंकि cosine की range \([-1,1]\) होती है, इसलिए इनपुट \(x\) का मान \([-1,1]\) में ही होगा। अतः \(\cos^{-1}x\) का domain \([ -1,1 ]\) है।
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