Question

What is the domain and range of `3sqrt( x^2 - 9)`?

Answer 1

Domain: `x<=-3` or `x>=3` also Domain: `(-oo,-3] uu [3, oo)`
Range: `[0, +oo)`

Explanation:

x can take on values -3 or less up to `-oo`
also x can take on values 3 or higher up to `+oo`

that is why Domain :`x<=-3` or `x>=3`

The lowest possible value is 0 up to `+oo` and that is the range .
That is if we let

`y=3*sqrt(x^2-9)`

when `x=+-3` the value of `y=0` and when `x` approaches a very high value, the value of `y` approaches a very high value also.

So the Range: `[0, +oo)`