Question

If f:[0, ∞) → [0, ∞) and f(x) = x/(x + 1), then f is

(a) one-to-one and onto 

(b) one-to-one but not onto. 

(c) onto but not one-to-one. 

(d) neither one-to-one nor onto.

Answer 1

Correct option (b) one-to-one but not onto.

Explanation:

f is monotonic function 

f is one-one function

Thus, R_f = R – {1} ≠ Co-domain 

Therefore f is not onto.