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What is the range of (f(x)=\frac{x}{x^2+1}) where (x\in\mathbb{R})?फलन (f(x)=\frac{x}{x^2+1}) का परिसर क्या है जहाँ (x\in\mathbb{R})?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: ( [-\frac{1}{2},\frac{1}{2}] )( [-\frac{1}{2},\frac{1}{2}] )
From (y=\frac{x}{x^2+1}), we get (yx^2-x+y=0), and discriminant (\ge0) gives (|y|\le\frac{1}{2}). The discriminant method is useful for range.(y=\frac{x}{x^2+1}) से (yx^2-x+y=0) मिलता है और विविक्तकर (\ge0) देने पर (|y|\le\frac{1}{2})। परिसर के लिए विविक्तकर विधि उपयोगी है।
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