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If \(f(x)=x^2-1\) and \(g(x)=x^2+1\), for which (x) is \(\left(\frac{f}{g}\right)(x)<1\) true?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?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: all \(x\in\mathbb{R}\)सभी \(x\in\mathbb{R}\)
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.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।
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