What is the domain and range of $g(x)=-sqrt(x^2-4)$ ?

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Answer 1 · 2017-02-27T17:32:36

Domain: $(-oo, -2], [2, oo)$
Range: $(-oo, 0]$

The domain is limited by the square root:

$x^2-4 >= 0$
$x^2 >=4$
$x<=-2 or x>=2$

The range limit comes from the domain:
When $x = -2 or x = 2, g(x) = 0$
When $x < -2 or x > 2, g(x) < 0$

So:
Domain: $(-oo, -2], [2, oo)$
Range: $(-oo, 0]$

What is the domain and range of g(x)=-sqrt(x^2-4)g(x)=-sqrt(x^2-4)?