The function f: [0, ∞) → [0, ∞) defined by f(x) = x/(1 + x) is
A
One-one and onto
B
One-one but not onto
C
Onto but not one-one
D
Neither one-one nor onto
Correct Option:
B
Explanation
For f(x) = x/(1 + x) with x ≥ 0, f'(x) = 1/(1 + x)² > 0, so the function is strictly increasing and therefore one-one. As x → ∞, f(x) → 1 without reaching 1, so the range is [0, 1), not the whole codomain [0, ∞). Hence it is not onto.
