Question

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

Answer 1

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

Explanation:

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]`