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

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

Question:

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

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

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:

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Given Data: -

  • The given radical function is: $$f\left( x \right) = \sqrt {9{x^2} - {x^3}} $$


The radical function {eq}f\left( x \right) = \sqrt...

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What is a Radical Function? - Definition, Equations & Graphs

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Chapter 7 / Lesson 3
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Learn about how to find the domain of a radical function. Read about graphing radical functions, the domain of radical function, and radical function equations.


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