Question

How do you find the domain of `f(x)=sqrt((x^2) -9x)`?

Answer 1

Domain of `x` is `(-oo, 0]` and `[9, oo)`

Explanation:

Well we know that for `f(x)inRR^n`:
`x^2-9x>=0`

Since that's the only inequality, solving for that will give the domain.
`x^2>=9x`
`x>=9`

And when `x>0`, `x^2-9x>=0` will always hold true, so:
`x<=0`

graph{sqrt(x^2-9x) [-28.42, 36.53, -1.3, 31.18]}

So, in interval notation, the domain of `x` is:

`(-oo, 0]` and `[9, oo)`
And `f(x)>=0`