The domain of $\sqrt x $ is $0\le x<\infty$
And its co-domain is $0\le y<\infty$
We know that the square root function is one-to-one since there exist only a unique $y$ such that $y^2=x$ since $y^2$ is a strictly increasing function. That is, $ z>y \implies z^2>y^2$.
But my question is whether the function $y=\sqrt x$ is surjective (onto) or not. Please explain it. Thanks.