Question

If the function $f:R\to$ A given by $f\left(x\right)=\frac{x^2}{x^2+1}$ is a surjection, then A is

• A. R
• B. [0,1]
• C. (0,1]
• D. [0,1)

Answer 1

The correct option is D [0,1)

$f\left(x\right)=\frac{x^2}{x^2+1}=1-\frac{1}{1+x^2}$
$x\to 0,f\left(x\right)\to 0$
$x\to \pm \infty ,f\left(x\right)\to 1$
$\therefore Aϵ[0,1)$