Let f : [ 0 , ∞ ) → [0,2] be defined by f ( x ) = 2 x 1 + x , then f is Options: A . &nbsp one – one but not onto B . &nbsp onto but not one – one C . &nbsp both one – one and onto D . &nbsp neither one – one nor onto

Let f:[0,∞)→ [0,2] be defined by f(x)=2x1+x , then f is

Question -

Let $f : [0, \infty) \to$ [0,2] be defined by $f (x) = \frac{2 x}{1 + x}$ , then f is

Options:

A . one – one but not onto

B . onto but not one – one

C . both one – one and onto

D . neither one – one nor onto

Answer: Option A
:
A
We can draw the graph and see that the given function is one - one.
Since, Range

⊏

Codomain

\Rightarrow

f is into

∴

f is only injective.

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