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

Question

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

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

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

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

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