whats the domain and range of y=square root x^2-4

Question

solomonzelman · Answer

$\normalsize\color{black}{ y=\sqrt{x^2-4}}$  like this ?

solomonzelman · Answer

The root can not be equal to a negative (it has to be zero or more). So we need that x² is less than 4.
Let's solve for that.     $\normalsize\color{black}{ │x│≥ 2}$                                                     $\LARGE\color{white}{  │}$
                                   $\normalsize\color{black}{ -2≥x~~~~~or~~~~~x≥ 2}$                                                     $\LARGE\color{white}{  │}$

solomonzelman · Answer

So it can be any real number less than or equal to -2, or any real number more than or equal to 2.