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If (f:\mathbb{R}\to\mathbb{R}), where (f(x)=\frac{x^2}{1+x^2}), why is (f) not onto?यदि (f:\mathbb{R}\to\mathbb{R}) जहाँ (f(x)=\frac{x^2}{1+x^2}), तो (f) आच्छादी क्यों नहीं है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Because its range is ([0,1))क्योंकि इसका परिसर ([0,1)) है
Step 1: Since (x^2\ge0), the value is at least (0). Step 2: Also (\frac{x^2}{1+x^2}<1), so (1) and larger values are not attained. Step 3: Compare numerator and denominator to understand the range.चरण 1: (x^2\ge0), इसलिए मान (0) या उससे बड़ा है। चरण 2: (\frac{x^2}{1+x^2}<1), इसलिए (1) और उससे बड़े मान नहीं मिलते। चरण 3: भिन्न में अंश-हर की तुलना से परिसर समझें।
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