Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Relations and Functions

Question:

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

Options:

one-one and onto

one-one but not onto

onto but not one-one

neither one-one nor onto

Correct Answer:

one-one but not onto

Explanation:

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.