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If \(f(x)=\frac{1}{x}\) and \(g(x)=\frac{1}{x+1}\), what are the correct form and domain of \(\left(\frac{f}{g}\right)(x)\)?यदि \(f(x)=\frac{1}{x}\) और \(g(x)=\frac{1}{x+1}\) हों, तो \(\left(\frac{f}{g}\right)(x)\) का सही रूप और प्रांत क्या होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(\frac{x+1}{x},\ x\ne 0,-1\)\(\frac{x+1}{x},\ x\ne 0,-1\)
Dividing gives \(\frac{1}{x}\div\frac{1}{x+1}=\frac{x+1}{x}\). The original (g) also requires (x\ne -1).भाग देने पर \(\frac{1}{x}\div\frac{1}{x+1}=\frac{x+1}{x}\) मिलता है। मूल (g) के लिए (x\ne -1) भी जरूरी है।
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