Let f:[0, ∞)→[0,2] be defined by f(x) = 2x/(1+x)=y, then f is :

The correct answer is Option (1) → One one but not onto

$y_1=y_2$

$⇒\frac{2x_1}{1+x_1}=\frac{2x_2}{1+x_2}⇒2x_1+2x_1x_2=2x_2+2x_1x_2$

$⇒x_1=x_2$ (one-one)

so $2x=yx+y$

so $x(2-y)=y⇒x=\frac{y}{2-y}$

so for $y=2$ x doesn't exist (Not onto)