Find the Domain f(x) = square root of 2x+5

$f (x) = \sqrt{2 x + 5}$

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 $x$ .

Subtract $5$ from both sides of the inequality.

$2 x \geq - 5$

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

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

Interval Notation:

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

Set-Builder Notation:

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