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For the inverse trigonometric function \(\cos^{-1}x\), what is the domain of \(\cos^{-1}x\)?व्युत्क्रम त्रिकोणमितीय फलन \(\cos^{-1}x\) 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 \(\cos y = x\). The cosine function has range \([-1,1]\). Therefore \(x\) can take values only in \([-1,1]\). Hence the domain of \(\cos^{-1}x\) is \([ -1,1 ]\).मान लीजिए \(y=\cos^{-1}x\). तब \(\cos y=x\). cosine फलन की range \([-1,1]\) होती है। इसलिए \(x\) का मान केवल \([-1,1]\) के बीच हो सकता है। अतः \(\cos^{-1}x\) का domain \([ -1,1 ]\) है।
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