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For the function \(y=\sin^{-1}x\), on which interval is \(y\) increasing?फल \(y=\sin^{-1}x\) के लिए \(y\) किस अंतराल पर बढ़ती (increasing) है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(\left[-1,1\right]\)\(\left[-1,1\right]\)
For \(y=\sin^{-1}x\), the principal range is chosen so that the inverse sine function is one-to-one. On its domain \(x\in\left[-1,1\right]\), \(\sin^{-1}x\) is strictly increasing, so it increases throughout \(\left[-1,1\right]\).\(y=\sin^{-1}x\) के लिए एक-एक (one-to-one) बनाने हेतु \(\sin^{-1}\) का principal range लिया जाता है। इसके domain \(x\in\left[-1,1\right]\) पर \(\sin^{-1}x\) सख्ती से (strictly) बढ़ती है, इसलिए यह पूरे \(\left[-1,1\right]\) पर बढ़ती है।
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