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If \(f:(0,\infty)\to\mathbb{R}\) and \(f(x)=x+\frac{1}{x}\), is (f) one-one?यदि \(f:(0,\infty)\to\mathbb{R}\) तथा \(f(x)=x+\frac{1}{x}\) हो तो (f) एकैकी है या नहीं?
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Correct answer:सही उत्तर: Noनहीं
Step 1: \(f(2)=2+\frac{1}{2}=\frac{5}{2}\). Step 2: \(f\left(\frac{1}{2}\right)=\frac{1}{2}+2=\frac{5}{2}\), while \(2\neq\frac{1}{2}\). Step 3: In functions involving (x) and \(\frac{1}{x}\), check reciprocal pairs carefully.चरण 1: \(f(2)=2+\frac{1}{2}=\frac{5}{2}\) है। चरण 2: \(f\left(\frac{1}{2}\right)=\frac{1}{2}+2=\frac{5}{2}\) है जबकि \(2\neq\frac{1}{2}\)। चरण 3: (x) और \(\frac{1}{x}\) वाले फलनों में ऐसे युग्म ध्यान से देखें।
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