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If \(f:\mathbb{R}\to (0,1)\), \(f(x)=\frac{1}{1+e^{-x}}\), what is the correct conclusion about (f)?यदि \(f:\mathbb{R}\to (0,1)\), \(f(x)=\frac{1}{1+e^{-x}}\), तो (f) के लिए सही निष्कर्ष क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Ontoआच्छादक है
Step 1: This function always gives a value between (0) and (1). Step 2: For every \(y\in(0,1)\), taking \(x=\ln\left(\frac{y}{1-y}\right)\) gives \(f(x)=y\). Step 3: In hard onto questions, solving for (x) from target (y) is very useful.चरण 1: यह फलन हमेशा (0) और (1) के बीच मान देता है। चरण 2: हर \(y\in(0,1)\) के लिए \(x=\ln\left(\frac{y}{1-y}\right)\) लेने पर \(f(x)=y\) मिलता है। चरण 3: कठिन आच्छादकता में लक्ष्य (y) से (x) निकालना बहुत उपयोगी है।
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