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Choose the correct option about (f:\mathbb{R}\to [0,1]), (f(x)=\frac{x^2}{1+x^2}).फलन (f:\mathbb{R}\to [0,1]), (f(x)=\frac{x^2}{1+x^2}) के बारे में सही विकल्प चुनिए।
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Not onto because (1) is not obtainedआच्छादक नहीं है क्योंकि (1) नहीं मिलता
Step 1: (\frac{x^2}{1+x^2}\ge 0) and it remains less than (1). Step 2: At (x=0), (0) is obtained, but (1) is never obtained for any real (x). Step 3: In closed codomains, always check whether endpoints are actually attained.चरण 1: (\frac{x^2}{1+x^2}\ge 0) और यह (1) से छोटा रहता है। चरण 2: (x=0) पर (0) मिलता है पर (1) किसी वास्तविक (x) से नहीं मिलता। चरण 3: बंद सहक्षेत्र में अंतिम बिंदु मिलते हैं या नहीं यह जरूर जाँचें।
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