Question

In Desmos: Write the domain in inequality notion y= 2 square root of x-2+4

Answer 1

Function is given as:

$y=\sqrt[2]{x^{-2}+4}$

$y=\sqrt[2]{\frac{1}{x^2}+4}$

for real solutions of y the term inside the square root should be as:

$\frac{1}{x^2}+4\ge0$

We can se that x has degree two so for all values of x the above term gives always positive values except x=0, as this makes it infinite value i.e. undefined, so the domain of the given equation is as:

Domain = ($-\infty,+\infty$ )-[0]