If f : [0, ∞) → [0, ∞) and $f(x) = \frac{x}{1+x}$, then f is

one-one and onto one-one but not onto onto but not one-one neither one-one nor onto

one-one but not onto

The given function is $f(x) = \frac{x}{1+x}=1-\frac{1}{1+x}$. Hence its range is [0, 1) which is a subset of [0, ∞). Also the function is one-one. Hence (B) is the correct answer.