Find the Domain y = square root of 2x-5

$y = \sqrt{2 x - 5}$

Set the radicand in $\sqrt{2 x - 5}$ greater than or equal to $0$ to find where the expression is defined.

$2 x - 5 \geq 0$

Solve for $x$ .

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Add $5$ to both sides of the inequality.

$2 x \geq 5$

Divide each term by $2$ and simplify.

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Divide each term in $2 x \geq 5$ by $2$ .

$\frac{2 x}{2} \geq \frac{5}{2}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$\frac{2 x}{2} \geq \frac{5}{2}$

Divide $x$ by $1$ .

$x \geq \frac{5}{2}$

The domain is all values of $x$ that make the expression defined.

Interval Notation:

$[\frac{5}{2}, \infty)$

Set-Builder Notation:

${x | x \geq \frac{5}{2}}$

Find the Domain y = square root of 2x-5

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