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If (f:\mathbb{R}\to[-\frac{1}{2},\frac{1}{2}]), (f(x)=\frac{x}{1+x^2}), which statement is correct?यदि (f:\mathbb{R}\to[-\frac{1}{2},\frac{1}{2}]), (f(x)=\frac{x}{1+x^2}) है, तो सही कथन कौन सा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: It is ontoयह आच्छादी है
Step 1: (f(x)=\frac{x}{1+x^2}) has maximum (\frac{1}{2}) at (x=1) and minimum (-\frac{1}{2}) at (x=-1). Step 2: All intermediate values are obtained by continuity. Step 3: If the codomain is a closed interval, check endpoints too.चरण 1: (f(x)=\frac{x}{1+x^2}) का अधिकतम (\frac{1}{2}) (x=1) पर और न्यूनतम (-\frac{1}{2}) (x=-1) पर है। चरण 2: बीच के सभी मान सततता के कारण मिलते हैं। चरण 3: बंद अंतराल सहप्रांत हो तो अंतिम बिंदुओं को भी जाँचें।
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