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Which statement is correct about \(f:(0,\infty)\to\mathbb{R}\), \(f(x)=x+\frac{1}{x}\)?फलन \(f:(0,\infty)\to\mathbb{R}\), \(f(x)=x+\frac{1}{x}\) के बारे में सही कथन कौन-सा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: It is not one-oneएकैकी नहीं है
Step 1: Look for two different positive values with the same image. Step 2: \(f(2)=\frac{5}{2}\) and \(f\left(\frac{1}{2}\right)=\frac{5}{2}\), while \(2\neq \frac{1}{2}\). Step 3: In functions like \(x+\frac{1}{x}\), notice the roles of (x) and \(\frac{1}{x}\).चरण 1: समान छवि के लिए दो अलग धनात्मक मान देखें। चरण 2: \(f(2)=\frac{5}{2}\) और \(f\left(\frac{1}{2}\right)=\frac{5}{2}\), जबकि \(2\neq \frac{1}{2}\)। चरण 3: \(x+\frac{1}{x}\) जैसे फलन में (x) और \(\frac{1}{x}\) की भूमिका ध्यान दें।
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