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