Proof of the image of a set $\mathbb R$ be the set of real numbers.
I have a set A = {$x$ ∈ $\mathbb R$ | $0< x$} . A function g : A --> $\mathbb R$ is defined by 
$f(x) = x^2
How do i prove whether the Image(A) = $\mathbb R$

Hint :
Take $g(x)=y$
$2xy-2x^2y=2x-1$
$(2y)x^2+x(2-2y)-1=0$.
Solve for $x$.
