Find the Domain f(x) = square root of 5x-30

$f (x) = \sqrt{5 x - 30}$

Step 1

Set the radicand in $\sqrt{5 x - 30}$ greater than or equal to $0$ to find where the expression is defined.

$5 x - 30 \geq 0$

Step 2

Solve for $x$ .

Add $30$ to both sides of the inequality.

$5 x \geq 30$

Divide each term in $5 x \geq 30$ by $5$ and simplify.

Divide each term in $5 x \geq 30$ by $5$ .

$\frac{5 x}{5} \geq \frac{30}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} \geq \frac{30}{5}$

Divide $x$ by $1$ .

$x \geq \frac{30}{5}$

Simplify the right side.

Divide $30$ by $5$ .

$x \geq 6$

Step 3

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

Interval Notation:

$[6, \infty)$

Set-Builder Notation:

${x | x \geq 6}$

Step 4