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If (f:\mathbb{R}\to\mathbb{R}) and (f(x)=e^x-e^{-x}), what is the nature of (f)?यदि (f:\mathbb{R}\to\mathbb{R}) तथा (f(x)=e^x-e^{-x}) है, तो (f) का स्वभाव क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: One-oneएक-एक
Step 1: (e^x) increases and (e^{-x}) decreases. Step 2: Therefore (e^x-e^{-x}) keeps increasing as (x) increases. Step 3: A strictly increasing function is one-one.चरण 1: (e^x) बढ़ता है और (e^{-x}) घटता है। चरण 2: इसलिए (e^x-e^{-x}) (x) बढ़ने पर लगातार बढ़ता है। चरण 3: लगातार बढ़ने वाला फलन एक-एक होता है।
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