Practicing Success
Practicing Success
CUET Preparation Today
Let $f:[0, ∞)→[0,2]$ be defined by $f(x) = \frac{2x}{1+x}=y$, then f is : |
One one but not onto onto but not one one both one one and onto neither one one nor onto |
One one but not onto |
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) |
