Find the set of all points at which the function is continuous.

{eq}f(x)=\sqrt{9x^2-x^3} {/eq}

Question:

Radical Function:

We check the continuity of a radical function using the graphing utility or using the radicand. We use a radical function's radicand to find the real values where the function is defined. If a radical function is {eq}y = \sqrt {ax + b} {/eq}, this function would be defined for real values when {eq}ax + b \ge 0. {/eq}

Similarly, we use the radicand of any radical function to define its domain and continuity.

Answer and Explanation: