Question
Question: If f : \[0, ∞) → \[0, ∞) and f (x) = \(\frac{x}{1 + x}\), then f is...
If f : [0, ∞) → [0, ∞) and f (x) = 1+xx, 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) = 1+xx = 1 –1+x1.
Hence its range is [0, 1) which is a subset of [0, ∞). Also the function is one-one