Find the Domain f(x) = square root of 3x-24

$f (x) = \sqrt{3 x - 24}$

Step 1

Set the radicand in $\sqrt{3 x - 24}$ greater than or equal to $0$ to find where the expression is defined.

$3 x - 24 \geq 0$

Step 2

Solve for $x$ .

Add $24$ to both sides of the inequality.

$3 x \geq 24$

Divide each term in $3 x \geq 24$ by $3$ and simplify.

Divide each term in $3 x \geq 24$ by $3$ .

$\frac{3 x}{3} \geq \frac{24}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} \geq \frac{24}{3}$

Divide $x$ by $1$ .

$x \geq \frac{24}{3}$

Simplify the right side.

Divide $24$ by $3$ .

$x \geq 8$

Step 3

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

Interval Notation:

$[8, \infty)$

Set-Builder Notation:

${x | x \geq 8}$

Step 4