Let \(f: R \rightarrow R\) be a function such that \(f(x)=\frac{x^2+2 x+1}{x^2+1}\). Then

\(f(x)\) is many-one in \((-\infty,-1)\)

\(f(x)\) is many-one in \((1, \infty)\)

\(f(x)\) is one-one in \([1, \infty)\) but not in \((-\infty, \infty)\)

\(f(x)\) is one-one in \((-\infty, \infty)\)