True or false: for all $x$ there is a $y$ such that if $x$ is non negative then $y^2 = x$ 
For all $x$ there is a $y$ such that if $x$ is non negative then $y^2 = x$

Is my logic correct in proving that statement is true ? Can provide an explanation of how to test this proof ?
$x=2$ then $y^2 = 2$
$x=2$ then $y = \sqrt 2$  
Truth table for this scenario
$t , t$
This proves there is $y$ such that $y^2 = x$


Define a function, $$f:\mathbb{R_{\geq 0}} \to \mathbb{R_{\geq 0}} $$ $$ x \mapsto \sqrt{x}$$
Injective:  $$\sqrt{x}=\sqrt{y} \Rightarrow x=y$$
Surjective:  $$Dom(f)= \{x| x\geq 0\}$$ $$y \in Ran(f) \Rightarrow y \geq 0 \Rightarrow y \in Dom(f)$$ \
$\textbf{Comment}$: I left out details for you to fill in. Comment if things are still unclear. Note $y^2 \in Dom(f), \Rightarrow \exists x$ s.t $\ x = (y)^2 \Rightarrow \sqrt{x} = y.$ 
