Question

What is the domain of the function `f(x) = sqrt{x^3 - 3x^2}`?

Answer 1

We can rewrite, and take squares out of the root

`=sqrt(x^2*(x-3))=xsqrt(x-3)`

Now the `(x-3)` under the root must be non-negative, so the domain is restricted to `x>=3` where `f(x)>=0`
graph{sqrt(x^3-3x^2) [-7.26, 24.77, -4.21, 11.82]}