1Cademy - Determining the Domain of the Radical Function $$f(x) = \sqrt{3x

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Domain of a Relation

Example

Determining the Domain of the Radical Function $f(x) = \sqrt{3x - 4}$

To precisely find the domain of the radical function $f(x) = \sqrt{3x - 4}$ , first note that the index of the radical is $2$ , which is an even number. For an even-indexed radical, the radicand must be greater than or equal to $0$ to successfully produce a real number. Set the radicand to be greater than or equal to $0$ : $3x - 4 \geq 0$ . Solving this inequality step-by-step gives $3x \geq 4$ , and then $x \geq \frac{4}{3}$ . Thus, the domain of the function consists of all values $x \geq \frac{4}{3}$ , which is accurately written in interval notation as $\left[\frac{4}{3}, \infty\right)$ .