If \(f:\mathbb{R}\to\mathbb{R}\) and \(f(x)=\frac{x}{1+x^2}\), is (f) one-one?

Correct answer: No

Step 1: To show that a function is not one-one, find two different inputs with the same output. Step 2: \(f(2)=\frac{2}{5}\) and \(f\left(\frac{1}{2}\right)=\frac{\frac{1}{2}}{1+\frac{1}{4}}=\frac{2}{5}\), while \(2\neq\frac{1}{2}\). Step 3: In fractional functions, reciprocal pairs can often give the same value.