x2+y-4=0 solve for x in getting the range of a function

x² + y - 4  =  0

If you want to solve for x:

Get the x-term alone on one side:

x²  =  4 - y

Then find the square root of both sides; remember that there are two answers:

x  =  √(4 - y)     or     x  =  -√(4 - y)  

However, you don't need to do this to find the range ...

Solving for y:  y  =  x² + 4

For any value of x, y must be at least 4 and can be any number greater than 4, so the range consists of  y  ≥  4.

$${{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{y}}{\mathtt{\,-\,}}{\mathtt{4}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}{\sqrt{{\mathtt{4}}{\mathtt{\,-\,}}{\mathtt{y}}}}\\ {\mathtt{x}} = {\sqrt{{\mathtt{4}}{\mathtt{\,-\,}}{\mathtt{y}}}}\\ \end{array} \right\}$$