Find the Domain f(x) = square root of 4x-32

$f (x) = \sqrt{4 x - 32}$

Step 1

Set the radicand in $\sqrt{4 x - 32}$ greater than or equal to $0$ to find where the expression is defined.

$4 x - 32 \geq 0$

Step 2

Solve for $x$ .

Add $32$ to both sides of the inequality.

$4 x \geq 32$

Divide each term in $4 x \geq 32$ by $4$ and simplify.

Divide each term in $4 x \geq 32$ by $4$ .

$\frac{4 x}{4} \geq \frac{32}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} \geq \frac{32}{4}$

Divide $x$ by $1$ .

$x \geq \frac{32}{4}$

Simplify the right side.

Divide $32$ by $4$ .

$x \geq 8$

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