Question

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

• 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 1

The correct option is A one – one but not onto

We can draw the graph and see that the given function is one - one.
Since, Range $⊏$ Codomain $\Rightarrow$ f is into
$\therefore$ f is only injective.