Find the Domain f(x) = square root of 5x-3

$f (x) = \sqrt{5 x - 3}$

Set the radicand in $\sqrt{5 x - 3}$ greater than or equal to $0$ to find where the expression is defined.

$5 x - 3 \geq 0$

Solve for $x$ .

Add $3$ to both sides of the inequality.

$5 x \geq 3$

Divide each term in $5 x \geq 3$ by $5$ and simplify.

Divide each term in $5 x \geq 3$ by $5$ .

$\frac{5 x}{5} \geq \frac{3}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} \geq \frac{3}{5}$

Divide $x$ by $1$ .

$x \geq \frac{3}{5}$

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

Interval Notation:

$[\frac{3}{5}, \infty)$

Set-Builder Notation:

${x | x \geq \frac{3}{5}}$