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Question

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

If f : [0, ∞) → [0, ∞) and f (x) = x1+x\frac{x}{1 + x}, then f is

A

One-one and onto

B

One-one but not onto

C

Onto but not one-one

D

Neither one-one nor onto

Answer

One-one but not onto

Explanation

Solution

The given function is f (x) = x1+x\frac{x}{1 + x} = 1 –11+x\frac{1}{1 + x}.

Hence its range is [0, 1) which is a subset of [0, ∞). Also the function is one-one