Question

If f : [0, ∞) →[ 0,∞) and f(x) = x/1 + x, 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(x) = x/1 + x  is one-to-one and into function. x₁,x₂ (0,∞), for one-to-one function.

 Now,

Range of f(x) ∈[0 ,1) and range of f(x) is not equal to co-domain. Hence, f(x) is not onto function.