JEE Math Practice Question

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

1. A.$$f(x)$$ is many-one in $$( - \infty , - 1)$$
2. B.$$f(x)$$ is one-one in $$( - \infty ,\infty )$$
3. C.$$f(x)$$ is one-one in $$[1,\infty )$$ but not in $$( - \infty ,\infty )$$
4. D.$$f(x)$$ is many-one in $$(1,\infty )$$