क्योंकि \(x^2+1>0\) और \(x^2-1<x^2+1\), अनुपात हमेशा (1) से छोटा है। धन हर होने पर असमता की दिशा नहीं बदलती। / Since \(x^2+1>0\) and \(x^2-1<x^2+1\), the ratio is always less than (1). With a positive denominator, the inequality direction does not change.
Mathematics Answer, Explanation and Revision Hints
यदि \(f(x)=x^2-1\) और \(g(x)=x^2+1\) हैं, तो \(\left(\frac{f}{g}\right)(x)<1\) किसके लिए सत्य है? / If \(f(x)=x^2-1\) and \(g(x)=x^2+1\), for which (x) is \(\left(\frac{f}{g}\right)(x)<1\) true?
Correct Answer: A. सभी \(x\in\mathbb{R}\) / all \(x\in\mathbb{R}\). Explanation: क्योंकि \(x^2+1>0\) और \(x^2-1<x^2+1\), अनुपात हमेशा (1) से छोटा है। धन हर होने पर असमता की दिशा नहीं बदलती। / Since \(x^2+1>0\) and \(x^2-1<x^2+1\), the ratio is always less than (1). With a positive denominator, the inequality direction does not change.
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