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

Apr 8, 2015

We can rewrite, and take squares out of the root

$= \sqrt{{x}^{2} \cdot \left(x - 3\right)} = x \sqrt{x - 3}$

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