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If \(f:\mathbb{R}\to \left[\frac{1}{2},1\right)\), \(f(x)=\frac{x^2+1}{x^2+2}\), what is the correct conclusion about \(f\)?यदि \(f:\mathbb{R}\to \left[\frac{1}{2},1\right)\), \(f(x)=\frac{x^2+1}{x^2+2}\), तो \(f\) के बारे में सही निष्कर्ष क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Ontoआच्छादक है
Step 1: Put \(t=x^2\ge0\), so the function becomes \(\frac{t+1}{t+2}\). Step 2: At \(t=0\), the value is \(\frac{1}{2}\), and as \(t\to\infty\), it approaches \(1\) without reaching it. Step 3: Replacing \(x^2\) by \(t\) simplifies hard range questions.चरण 1: \(t=x^2\ge0\) रखने पर फलन \(\frac{t+1}{t+2}\) बनता है। चरण 2: \(t=0\) पर \(\frac{1}{2}\) और \(t\to\infty\) पर मान \(1\) के पास जाता है पर \(1\) नहीं आता। चरण 3: \(x^2\) को \(t\) मानकर कठिन परास प्रश्न सरल हो जाते हैं।
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